Another issue Facebook ran into was that npm is, by design, nondeterministic — yet Facebook's engineers needed a consistent and reliable system for their DevOps workflow.
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Nondeterministic visibly pushdown automata are as expressive as deterministic ones. Hence one can transform a nondeterministic visibly pushdown automaton into a deterministic one, but if the nondeterministic automaton had s states, the deterministic one may have up to 2^{s^2} states.
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In automata theory, an alternating tree automaton (ATA) is an extension of nondeterministic tree automaton as same as alternating finite automaton extends nondeterministic finite automaton (NFA).
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Therefore a nondeterministic protocol which solves the problem cannot exist.
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Often in computational theory, the term "algorithm" refers to a deterministic algorithm. A nondeterministic algorithm is different from its more familiar deterministic counterpart in its ability to arrive at outcomes using various routes. If a deterministic algorithm represents a single path from an input to an outcome, a nondeterministic algorithm represents a single path stemming into many paths, some of which may arrive at the same output and some of which may arrive at unique outputs. This property is captured mathematically in "nondeterministic" models of computation such as the nondeterministic finite automaton.
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This is in sharp contrast to automata on infinite words, where nondeterministic Büchi ω-automata have the same expressive power as the others. The languages of nondeterministic Muller/Rabin/Streett/parity tree automata are closed under union, intersection, projection, and complementation.
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A probabilistic Turing machine is a type of nondeterministic Turing machine in which each nondeterministic step is a "coin-flip", that is, at each step there are two possible next moves and the Turing machine probabilistically selects which move to take.
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A comparison of deterministic and nondeterministic computation. If any branch on the nondeterministic computation accepts then the NTM accepts. A variant of the deterministic Turing machine (DTM) is the nondeterministic Turing machine (NTM). Intuitively, an NTM is just a regular Turing machine that has the added capability of being able to explore multiple possible future actions from a given state, and "choosing" a branch that accepts (if any accept).
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DFAs can be built from nondeterministic finite automata (NFAs) using the powerset construction method.
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The nondeterministic decision tree complexity of a function is known more commonly as the certificate complexity of that function. It measures the number of input bits that a nondeterministic algorithm would need to look at in order to evaluate the function with certainty.
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The syntax is based on the use of regular expressions. See also nondeterministic finite automaton.
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Powerset construction is an algorithm to construct a deterministic finite automaton from a given nondeterministic finite automaton.
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In denotational semantics and domain theory, power domains are domains of nondeterministic and concurrent computations. The idea of power domains for functions is that a nondeterministic function may be described as a deterministic set-valued function, where the set contains all values the nondeterministic function can take for a given argument. For concurrent systems, the idea is to express the set of all possible computations. Roughly speaking, a power domain is a domain whose elements are certain subsets of a domain.
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In the theory of computation, a generalized nondeterministic finite automaton (GNFA), also known as an expression automaton or a generalized nondeterministic finite state machine, is a variation of a nondeterministic finite automaton (NFA) where each transition is labeled with any regular expression. The GNFA reads blocks of symbols from the input which constitute a string as defined by the regular expression on the transition. There are several differences between a standard finite state machine and a generalized nondeterministic finite state machine. A GNFA must have only one start state and one accept state, and these cannot be the same state, whereas a NFA or DFA both may have several accept states, and the start state can be an accept state.
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As with string automata, a TWA may be deterministic or nondeterministic. More formally, a (nondeterministic) tree-walking automaton over an alphabet Σ is a tuple where Q is a finite set of states, its subsets I, F, and R are the sets of initial, accepting and rejecting states, respectively, and is the transition relation.
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The languages of this class have great practical importance in computer science as they can be parsed much more efficiently than nondeterministic context-free languages. The complexity of the program and execution time of a deterministic pushdown automaton is vastly less than that of a nondeterministic one. In the naive implementation, the latter must make copies of the stack every time a nondeterministic step occurs. The best known algorithm to test membership in any context-free language is Valiant's algorithm, taking O(2.378) time, where is the length of the string.
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In computer science, Thompson's construction algorithm, also called the McNaughton-Yamada-Thompson algorithm, is a method of transforming a regular expression into an equivalent nondeterministic finite automaton (NFA). This NFA can be used to match strings against the regular expression. This algorithm is credited to Ken Thompson. Regular expressions and nondeterministic finite automata are two representations of formal languages.
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He also invented Thompson's construction algorithm used for converting regular expression into nondeterministic finite automaton in order to make expression matching faster.
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NP problem, which (among other equivalent formulations) concerns the question of how difficult it is to simulate nondeterministic computation with a deterministic computer.
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This definition still retains the asymmetry that any nondeterministic branch can accept, but every branch must reject for the string to be rejected.
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Although the original definition of fine-grained reductions involved deterministic algorithms, the corresponding concepts for randomized algorithms and nondeterministic algorithms have also been considered.
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In most practical cases deterministic algorithms or randomized algorithms are discussed, although theoretical computer science also considers nondeterministic algorithms and other advanced models of computation.
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Nondeterministic Turing machines have only bounded nondeterminism. Likewise sequential programs containing guarded commands as the only sources of nondeterminism have only bounded nondeterminism (Edsger Dijkstra [1976]). Briefly, choice nondeterminism is bounded. Gordon Plotkin gave a proof in his original 1976 paper on powerdomains: :Now the set of initial segments of execution sequences of a given nondeterministic program , starting from a given state, will form a tree.
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For example, Savitch's theorem proves that no problem that requires exponential space for a deterministic Turing machine can be solved by a nondeterministic polynomial space Turing machine.
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In 1960, John Myhill introduced an automaton model today known as deterministic linear bounded automaton. In 1963, Peter S. Landweber proved that the languages accepted by deterministic LBAs are context-sensitive. In 1964, S.-Y. Kuroda introduced the more general model of (nondeterministic) linear bounded automata, noted that Landweber's proof also works for nondeterministic linear bounded automata, and showed that the languages accepted by them are precisely the context-sensitive languages.
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Nondeterministic Muller, Rabin, Streett, and parity tree automata recognize the same set of tree languages, and thus have the same expressive power. But nondeterministic Büchi tree automata are strictly weaker, i.e., there exists a tree language that can be recognized by a Rabin tree automaton but cannot be recognized by any Büchi tree automaton.Rabin, M. O.: Weakly definable relations and special automata,Mathematical logic and foundation of set theory, pp.
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In some scenarios, all possible paths are allowed to run simultaneously. In algorithm design, nondeterministic algorithms are often used when the problem solved by the algorithm inherently allows multiple outcomes (or when there is a single outcome with multiple paths by which the outcome may be discovered, each equally preferable). Crucially, every outcome the nondeterministic algorithm produces is valid, regardless of which choices the algorithm makes while running. In computational complexity theory, nondeterministic algorithms are ones that, at every possible step, can allow for multiple continuations (imagine a person walking down a path in a forest and, every time they step further, they must pick which fork in the road they wish to take).
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The global state approach was continued in automata theory for finite-state machines and push down stack machines, including their nondeterministic versions. Such nondeterministic automata have the property of bounded nondeterminism; that is, if a machine always halts when started in its initial state, then there is a bound on the number of states in which it halts. Edsger Dijkstra further developed the nondeterministic global state approach. Dijkstra's model gave rise to a controversy concerning unbounded nondeterminism (also called unbounded indeterminacy), a property of concurrency by which the amount of delay in servicing a request can become unbounded as a result of arbitration of contention for shared resources while still guaranteeing that the request will eventually be serviced.
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Parsimonious reductions are defined for problems in nondeterministic complexity classes such as NP, which contains problems whose candidate solutions can be verified by a polynomial time deterministic Turing machine.
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In nondeterministic communication complexity, Alice and Bob have access to an oracle. After receiving the oracle's word, the parties communicate to deduce f(x,y). The nondeterministic communication complexity is then the maximum over all pairs (x,y) over the sum of number of bits exchanged and the coding length of the oracle word. Viewed differently, this amounts to covering all 1-entries of the 0/1-matrix by combinatorial 1-rectangles (i.e.
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This class also sees use in the field of pseudorandomness and derandomization, where researchers consider the open problem of whether L = RL.. The corresponding nondeterministic space complexity class is NL.
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In formal language theory, and in particular the theory of nondeterministic finite automata, it is known that the union of two regular languages is a regular language. This article provides a proof of that statement.
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In computational complexity theory, the complexity class TFNP is the class of total function problems which can be solved in nondeterministic polynomial time. That is, it is the class of function problems that are guaranteed to have an answer, and this answer can be checked in polynomial time, or equivalently it is the subset of FNP where a solution is guaranteed to exist. The abbreviation TFNP stands for "Total Function Nondeterministic Polynomial". TFNP contains many natural problems that are of interest to computer scientists.
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25): Minsky states that although a machine may be finite, and finite automata "have a number of theoretical limitations": :...the magnitudes involved should lead one to suspect that theorems and arguments based chiefly on the mere finiteness [of] the state diagram may not carry a great deal of significance. (Minsky p. 25) It can also be decided automatically whether a nondeterministic machine with finite memory halts on none, some, or all of the possible sequences of nondeterministic decisions, by enumerating states after each possible decision.
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The nondeterministic algorithms are often used to find an approximation to a solution, when the exact solution would be too costly to obtain using a deterministic one. The notion was introduced by Robert W. Floyd in 1967.
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A nondeterministic algorithm for determining whether a 2-satisfiability instance is not satisfiable, using only a logarithmic amount of writable memory, is easy to describe: simply choose (nondeterministically) a variable v and search (nondeterministically) for a chain of implications leading from v to its negation and then back to v. If such a chain is found, the instance cannot be satisfiable. By the Immerman–Szelepcsényi theorem, it is also possible in nondeterministic logspace to verify that a satisfiable 2-satisfiability instance is satisfiable. 2-satisfiability is NL-complete,.
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Aizikowitz and Kaminski introduced a new class of pushdown automata (PDA) called synchronized alternating pushdown automata (SAPDA). They proved it to be equivalent to conjunctive grammars in the same way as nondeterministic PDAs are equivalent to context-free grammars.
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Antwerp: ICALP, 1984 Boundedness, deadlocks, and unspecified reception state are all decidable in polynomial time (which means that a particular problem can be solved in tractable, not infinite, amount of time) since the decision problems regarding them are nondeterministic logspace complete.
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Then he argued that , where is the empty stream. Now }, so it must be that is an element of , a contradiction. He concluded that: :It appears that a fair merge cannot be written as a nondeterministic data flow program operating on streams.
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Machine actions include pushing, popping, or replacing the stack top. A deterministic pushdown automaton has at most one legal transition for the same combination of input symbol, state, and top stack symbol. This is where it differs from the nondeterministic pushdown automaton.
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Géraud Sénizergues (1997) proved that the equivalence problem for deterministic PDA (i.e. given two deterministic PDA A and B, is L(A)=L(B)?) is decidable, -- Full version: a proof that earned him the 2002 Gödel Prize. For nondeterministic PDA, equivalence is undecidable.
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Translation as 'The actual content of quantum theoretical kinematics and mechanics' here However, if collapse were a fundamental physical phenomenon, rather than just the epiphenomenon of some other process, it would mean nature was fundamentally stochastic, i.e. nondeterministic, an undesirable property for a theory.
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A given input string may drive a nondeterministic pushdown automaton to one of several configuration sequences; if one of them leads to an accepting configuration after reading the complete input string, the latter is said to belong to the language accepted by the automaton.
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Event manipulation for Nondeterministic Shared- Memory Programs / High-Performance Computing and Networking. 9th International Conference, HPCN Europe 2001, Amsterdam, The Netherlands, June 25–27, 2001, This type of bug is known colloquially as a Heisenbug, by analogy with the observer effect in quantum mechanics.
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In computer science theory – particularly formal language theory – the Glushkov Construction Algorithm, invented by Victor Mikhailovich Glushkov, transforms a given regular expression into an equivalent nondeterministic finite automaton (NFA). Thus, it forms a bridge between regular expressions and nondeterministic finite automata: two abstract representations of the same class of formal languages. A regular expression may be used to conveniently describe an advanced search pattern in a "find and replace"–like operation of a text processing utility. Glushkov's algorithm can be used to transform it into an NFA, which furthermore is small by nature, as the number of its states equals the number of symbols of the regular expression, plus one.
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The two definitions of NP as the class of problems solvable by a nondeterministic Turing machine (TM) in polynomial time and the class of problems verifiable by a deterministic Turing machine in polynomial time are equivalent. The proof is described by many textbooks, for example Sipser's Introduction to the Theory of Computation, section 7.3. To show this, first suppose we have a deterministic verifier. A nondeterministic machine can simply nondeterministically run the verifier on all possible proof strings (this requires only polynomially many steps because it can nondeterministically choose the next character in the proof string in each step, and the length of the proof string must be polynomially bounded).
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L. Babai, L. Fortnow, and C. Lund. Nondeterministic exponential time has two-prover interactive protocols. Computational Complexity, 1(1):3-40, 1991. These algebraic techniques were expanded further by Fortnow, Babai, Leonid Levin, and Mario Szegedy when they presented a new generic mechanism for checking computations.
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MCTS algorithm has also been used in programs that play other board games (for example Hex, Havannah, Game of the Amazons, and Arimaa), real-time video games (for instance Ms. Pac-Man and Fable Legends), and nondeterministic games (such as skat, poker, Magic: The Gathering, or Settlers of Catan).
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In computer science, in particular in formal language theory, a quotient automaton can be obtained from a given nondeterministic finite automaton by joining some of its states. The quotient recognizes a superset of the given automaton; in some cases, handled by the Myhill–Nerode theorem, both languages are equal.
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The DFAs are closed under the following operations. For each operation, an optimal construction with respect to the number of states has been determined in state complexity research. Since DFAs are equivalent to nondeterministic finite automata (NFA), these closures may also be proved using closure properties of NFA.
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These differ in the choice of Accessibility relation. (P always means "P is true at the current computer state".) These two examples involve nondeterministic or not-fully-understood computations; there are many other modal logics specialized to different types of program analysis. Each one naturally leads to slightly different axioms.
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With Paul Erdős, he proved the Erdős–Szemerédi theorem on the number of sums and products in a finite set. With Wolfgang Paul, Nick Pippenger, and William Trotter, he established a separation between nondeterministic linear time and deterministic linear time, in the spirit of the infamous P versus NP problem.
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In addition, it is difficult to use a test suite to test behavior that is intended or allowed to be nondeterministic. Therefore, in common practice, test suites are used only in combination with one of the other language specification techniques, such as a natural language description or a reference implementation.
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State complexity is an area of theoretical computer science dealing with the size of abstract automata, such as different kinds of finite automata. The classical result in the area is that simulating an n-state nondeterministic finite automaton by a deterministic finite automaton requires exactly 2^n states in the worst case.
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Also known as Petri nets, this conceptual modeling technique allows a system to be constructed with elements that can be described by direct mathematical means. The petri net, because of its nondeterministic execution properties and well defined mathematical theory, is a useful technique for modeling concurrent system behavior, i.e. simultaneous process executions.
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The Church–Rosser property of the lambda calculus means that evaluation (β-reduction) can be carried out in any order, even in parallel. This means that various nondeterministic evaluation strategies are relevant. However, the lambda calculus does not offer any explicit constructs for parallelism. One can add constructs such as Futures to the lambda calculus.
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Using a random or pseudorandom bit (a pure guess) would guarantee every branch a 50% correct prediction rate, which cannot be improved (or worsened) by reordering instructions. (With the simplest static prediction of "assume take", compilers can reorder instructions to get better than 50% correct prediction.) Also, it would make timing [much more] nondeterministic.
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Euler diagram for P, NP, NP-complete, and NP-hard set of problems. Under the assumption that P≠NP, the existence of problems within NP but outside both P and NP-complete was established by Ladner. Corollary 1.1. In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems.
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Orc is a concurrent, nondeterministic computer programming language created by Jayadev Misra at the University of Texas at Austin. Orc provides uniform access to computational services, including distributed communication and data manipulation, through sites. Using four simple concurrency primitives, the programmer orchestrates the invocation of sites to achieve a goal, while managing timeouts, priorities, and failures.
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The space hierarchy theorems are separation results that show that both deterministic and nondeterministic machines can solve more problems in (asymptotically) more space, subject to certain conditions. For example, a deterministic Turing machine can solve more decision problems in space n log n than in space n. The somewhat weaker analogous theorems for time are the time hierarchy theorems.
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Nondeterministic finite automaton with ε-moves (NFA-ε) is a further generalization to NFA. This automaton replaces the transition function with the one that allows the empty string ε as a possible input. The transitions without consuming an input symbol are called ε-transitions. In the state diagrams, they are usually labeled with the Greek letter ε.
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MultiLisp is a functional programming language, a dialect of the language Lisp, and of its dialect Scheme, extended with constructs for parallel computing execution and shared memory. These extensions involve side effects, rendering MultiLisp nondeterministic. Along with its parallel-programming extensions, MultiLisp also had some unusual garbage collection and task scheduling algorithms. Like Scheme, MultiLisp was optimized for symbolic computing.
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In automata theory, an unambiguous finite automaton (UFA) is a nondeterministic finite automaton (NFA) such that each word has at most one accepting path. Each deterministic finite automaton (DFA) is an UFA, but not vice versa. DFA, UFA, and NFA recognize exactly the same class of formal languages. On the one hand, an NFA can be exponentially smaller than an equivalent DFA.
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There are several ways an algorithm may behave differently from run to run. A concurrent algorithm can perform differently on different runs due to a race condition. A probabilistic algorithm's behaviors depends on a random number generator. An algorithm that solves a problem in nondeterministic polynomial time can run in polynomial time or exponential time depending on the choices it makes during execution.
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Each of the steps of this algorithm can be done in time linear in the automaton size, hence the algorithm is clearly optimal. ; Minimization The algorithm for minimizing nondeterministic finite automaton also correctly minimizes a Büchi automaton. The algorithm does not guarantee minimum Büchi automaton . However, the algorithms for minimizing deterministic finite automaton does not work for deterministic Büchi automaton.
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For computational processes that are nondeterministic (in the sense of being probabilistic or random), the relation between old and new states is not a single-valued function, and the requirement needed to obtain physical reversibility becomes a slightly weaker condition, namely that the size of a given ensemble of possible initial computational states does not decrease, on average, as the computation proceeds forwards.
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A GNFA must have only one transition between any two states, whereas a NFA or DFA both allow for numerous transitions between states. In a GNFA, a state has a single transition to every state in the machine, although often it is a convention to ignore the transitions that are labelled with the empty set when drawing generalized nondeterministic finite state machines.
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A further distinction is between deterministic (DFA) and non-deterministic (NFA, GNFA) automata. In a deterministic automaton, every state has exactly one transition for each possible input. In a non-deterministic automaton, an input can lead to one, more than one, or no transition for a given state. The powerset construction algorithm can transform any nondeterministic automaton into a (usually more complex) deterministic automaton with identical functionality.
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It is possible to draw a state diagram from a state- transition table. A sequence of easy to follow steps is given below: # Draw the circles to represent the states given. # For each of the states, scan across the corresponding row and draw an arrow to the destination state(s). There can be multiple arrows for an input character if the finite-state machine is nondeterministic.
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In other words, non-trivial propensities (those that differ from 0 and 1) only exist for genuinely nondeterministic experiments. A number of other philosophers, including David Miller and Donald A. Gillies, have proposed propensity theories somewhat similar to Popper's. Other propensity theorists (e.g. Ronald Giere) do not explicitly define propensities at all, but rather see propensity as defined by the theoretical role it plays in science.
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On the other hand, a triply exponential upper bound on a decision procedure for Presburger Arithmetic was proved by Oppen (1978). A more tight complexity bound was shown using alternating complexity classes by . The set of true statements in Presburger arithmetic (PA) is shown complete for TimeAlternations(22nO(1), n). Thus, its complexity is between double exponential nondeterministic time (2-NEXP) and double exponential space (2-EXPSPACE).
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In theoretical computer science, in particular in formal language theory, Kleene's algorithm transforms a given nondeterministic finite automaton (NFA) into a regular expression. Together with other conversion algorithms, it establishes the equivalence of several description formats for regular languages. Alternative presentations of the same method include the "elimination method" attributed to Brzozowski and McCluskey, the algorithm of McNaughton and Yamada, and the use of Arden's lemma.
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In fact, this is so helpful that Babai, Fortnow, and Lund were able to show that MIP = NEXPTIME, the class of all problems solvable by a nondeterministic machine in exponential time, a very large class. Moreover, all languages in NP have zero-knowledge proofs in an MIP system, without any additional assumptions; this is only known for IP assuming the existence of one-way functions.
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In automata theory (a branch of theoretical computer science), NFA minimization is the task of transforming a given nondeterministic finite automaton (NFA) into an equivalent NFA that has a minimum number of states, transitions, or both. While efficient algorithms exist for DFA minimization, NFA minimization is NP-hard. No efficient (polynomial time) algorithms are known. Nonetheless, algorithms exist which implement useful functionality such as Kameda-Weiner.
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Marek Chrobak is a full professor at University of California, Riverside. He is known for his work competitive analysis of online algorithms, particularly for the k-server problem, on information dissemination in ad-hoc radio networks, and on graph drawing. In automata theory, Chrobak is known for his contributions to the study of finite automata over a one-letter alphabet. In particular, "Chrobak normal form" for nondeterministic finite automata is known.
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The standard reference for padding in space complexity (which predates this theorem) is . For a stronger padding argument that applies even to sublogarithmic space complexity classes, see . The result solved the second LBA problem. In other words, if a nondeterministic machine can solve a problem, another machine with the same resource bounds can solve its complement problem (with the yes and no answers reversed) in the same asymptotic amount of space.
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A race condition can be difficult to reproduce and debug because the end result is nondeterministic and depends on the relative timing between interfering threads. Problems of this nature can therefore disappear when running in debug mode, adding extra logging, or attaching a debugger. Bugs that disappear like this during debugging attempts are often referred to as a "Heisenbug". It is therefore better to avoid race conditions by careful software design.
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Several variants of this model are also equivalent to DFAs. In particular, the nondeterministic case (in which the transition from one state can be to multiple states given the same input) is reducible to a DFA. Other variants of this model allow more computational complexity. With a single infinite stack the model can parse (at least) any language that is computable by a Turing machine in linear time.
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There is a proliferation of Side-channel attack plaguing modern computer architecture. Many of these attacks measure slight, nondeterministic variations in the execution of some code, so the attacker needs many, possibly tens of thousands, of measurements to learn secrets. However, the Microscope attack allows a malicious OS to replay code an arbitrary number of times regardless of the programs actual structure, enabling dozens of side-channel attacks.
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Thue ( ) is an esoteric programming language invented by John Colagioia in early 2000. It is a meta-language that can be used to define or recognize Type-0 languages from the Chomsky hierarchy. Because it is able to define languages of such complexity, it is also Turing-complete itself. Thue is based on a nondeterministic string rewriting system called semi-Thue grammar, which itself is named after the Norwegian mathematician Axel Thue.
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One way to simulate a nondeterministic algorithm N using a deterministic algorithm D is to treat sets of states of N as states of D. This means that D simultaneously traces all the possible execution paths of N (see powerset construction for this technique in use for finite automata). Another is randomization, which consists of letting all choices be determined by a random number generator. The result is called a probabilistic deterministic algorithm.
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In computational complexity theory, NL-complete is a complexity class containing the languages that are complete for NL, the class of decision problems that can be solved by a nondeterministic Turing machine using a logarithmic amount of memory space. The NL-complete languages are the most "difficult" or "expressive" problems in NL. If a method exists for solving any one of the NL-complete problems in logarithmic memory space, then NL = L.
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In computer science, a graph-structured stack (GSS) is a directed acyclic graph where each directed path represents a stack. The graph-structured stack is an essential part of Tomita's algorithm, where it replaces the usual stack of a pushdown automaton. This allows the algorithm to encode the nondeterministic choices in parsing an ambiguous grammar, sometimes with greater efficiency. In the following diagram, there are four stacks: {7,3,1,0}, {7,4,1,0}, {7,5,2,0}, and {8,6,2,0}.
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In computational complexity theory, ' is the set of all decision problems solvable by a deterministic Turing machine in exponential space, i.e., in O(2^{p(n)}) space, where p(n) is a polynomial function of n. Some authors restrict p(n) to be a linear function, but most authors instead call the resulting class . If we use a nondeterministic machine instead, we get the class , which is equal to by Savitch's theorem.
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There is a direct one-to-one correspondence between the rules of a (strictly) right regular grammar and those of a nondeterministic finite automaton, such that the grammar generates exactly the language the automaton accepts.Hopcroft and Ullman 1979, p.218-219, Theorem 9.1 and 9.2 Hence, the right regular grammars generate exactly all regular languages. The left regular grammars describe the reverses of all such languages, that is, exactly the regular languages as well.
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In computational complexity theory, the complexity class ⊕P (pronounced "parity P") is the class of decision problems solvable by a nondeterministic Turing machine in polynomial time, where the acceptance condition is that the number of accepting computation paths is odd. An example of a ⊕P problem is "does a given graph have an odd number of perfect matchings?" The class was defined by Papadimitriou and Zachos in 1983.C. H. Papadimitriou and S. Zachos.
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Differences in how programming languages handle deallocation of memory is another issue when trying create interoperability. Manual and automatic deallocation is not the only issue but if it has deterministic and nondeterministic destruction. Based on the constraints of the language there are many different strategies for bridging the different behaviors. C++ which uses manual deallocation could use a Java styled garbage collector by changing deallocation behavior to delete the object, but not reclaim the memory.
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The observability of quantum jumps was predicted by Hans Dehmelt in 1975, and they were first observed using trapped ions of mercury at NIST in 1986. In 2019, it was demonstrated in an experiment with a superconducting artificial atom consisting of two strongly-hybridized transmon qubits placed inside a readout resonator cavity at 15 mK, that the evolution of some jumps is continuous, coherent, deterministic, and reversible. On the other hand other quantum jumps are inherently unpredictable ie. nondeterministic.
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In natural language processing, deterministic parsing refers to parsing algorithms that do not backtrack. LR-parsers are an example. (This meaning of the words "deterministic" and "non-deterministic" differs from that used to describe nondeterministic algorithms.) The deterministic behavior is desired and expected in compiling programming languages. In natural language processing, it was thought for a long time that deterministic parsing is impossible due to ambiguity inherent in natural languages (many sentences have more than one plausible parse).
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In the theory of computation, a branch of theoretical computer science, a pushdown automaton (PDA) is a type of automaton that employs a stack. Pushdown automata are used in theories about what can be computed by machines. They are more capable than finite-state machines but less capable than Turing machines. Deterministic pushdown automata can recognize all deterministic context-free languages while nondeterministic ones can recognize all context-free languages, with the former often used in parser design.
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Every context-free grammar can be transformed into an equivalent nondeterministic pushdown automaton. The derivation process of the grammar is simulated in a leftmost way. Where the grammar rewrites a nonterminal, the PDA takes the topmost nonterminal from its stack and replaces it by the right-hand part of a grammatical rule (expand). Where the grammar generates a terminal symbol, the PDA reads a symbol from input when it is the topmost symbol on the stack (match).
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For a context-free grammar in Greibach normal form, defining (1,γ) ∈ δ(1,a,A) for each grammar rule A → aγ also yields an equivalent nondeterministic pushdown automaton. The converse, finding a grammar for a given PDA, is not that easy. The trick is to code two states of the PDA into the nonterminals of the grammar. Theorem. For each pushdown automaton M one may construct a context- free grammar G such that N(M)=L(G).
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In mathematics and computer science, the probabilistic automaton (PA) is a generalization of the nondeterministic finite automaton; it includes the probability of a given transition into the transition function, turning it into a transition matrix. Thus, the probabilistic automaton also generalizes the concepts of a Markov chain and of a subshift of finite type. The languages recognized by probabilistic automata are called stochastic languages; these include the regular languages as a subset. The number of stochastic languages is uncountable.
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In the 1960s, theoretical research in computer science on regular expressions and finite automata led to the discovery that context-free grammars are equivalent to nondeterministic pushdown automata. These grammars were thought to capture the syntax of computer programming languages. The first computer programming languages were under development at the time (see History of programming languages) and writing compilers was difficult. But using context-free grammars to help automate the parsing part of the compiler simplified the task.
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A nondeterministic Turing machine can move to a state that is not determined by the previous state. Such a machine could solve an NP problem in polynomial time by falling into the correct answer state (by luck), then conventionally verifying it. Such machines are not practical for solving realistic problems but can be used as theoretical models. An answer to the P = NP question would determine whether problems that can be verified in polynomial time can also be solved in polynomial time.
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A nondeterministic protocol with a potentially variable message count can be compared to an edge-labeled finite tree, where each node in the tree represents an explored example up to a specified point. A protocol that terminates before sending any messages is represented by a tree containing only a root node. The edges from a node to each child are labeled with the messages sent in order to reach the child state. Leaf nodes represent points at which the protocol terminates.
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Suppose there exists a nondeterministic protocol P which solves the Two Generals' Problem. Then, by a similar argument to the one used for fixed-length deterministic protocols above, P' must also solve the Two Generals' Problem, where the tree representing P' is obtained from that for P by removing all leaf nodes and the edges leading to them. Since P is finite, it then follows that the protocol that terminates before sending any messages would solve the problem. But clearly it does not.
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Minimal solution of the hardest initial Rush Hour configuration. When generalized so that it can be played on an arbitrarily large board, the problem of deciding if a Rush Hour problem has a solution is PSPACE-complete. This is proved by reducing a graph game called nondeterministic constraint logic, which is known to be PSPACE-complete, to generalized Rush Hour positions. In 2005, Tromp and Cilibrasi showed that Rush Hour is still PSPACE-complete when the cars are of size 2 only.
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The misuse of technical terms to produce howlers is so common that it often goes unnoticed except by people skilled in the relevant fields. One case in point is the use of "random", when the intended meaning is adventitious, arbitrary, accidental, or something similarly uncertain or nondeterministic. Another example is to speak of something as infinite when the intended meaning is: "very large". Some terms have been subject to such routine abuse that they lose their proper meanings, reducing their expressive value.
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The automaton can alternatively ignore the stack, and leave it as it is. Put together: Given an input symbol, current state, and stack symbol, the automaton can follow a transition to another state, and optionally manipulate (push or pop) the stack. If, in every situation, at most one such transition action is possible, then the automaton is called a deterministic pushdown automaton (DPDA). In general, if several actions are possible, then the automaton is called a general, or nondeterministic, PDA.
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These algorithms do not arrive at a solution for every possible computational path; however, they are guaranteed to arrive at a correct solution for some path (i.e., the person walking through the forest may only find their cabin if they pick some combination of "correct" paths). The choices can be interpreted as guesses in a search process. A large number of problems can be conceptualized through nondeterministic algorithms, including the most famous unresolved question in computing theory, P vs NP.
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In theoretical computer science, a nondeterministic Turing machine (NTM) is a theoretical model of computation whose governing rules specify more than one possible action when in some given situations. That is, an NTM's next state is not completely determined by its action and the current symbol it sees (unlike a deterministic Turing machine). NTMs are sometimes used in thought experiments to examine the abilities and limitations of computers. One of the most important open problems in theoretical computer science is the P vs.
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It is known that and also, by the time hierarchy theorem and the space hierarchy theorem, that so at least one of the first three inclusions and at least one of the last three inclusions must be proper, but it is not known which ones are. Most experts believe all the inclusions are proper. It is also known that if P = NP, then EXPTIME NEXPTIME, the class of problems solvable in exponential time by a nondeterministic Turing machine. Section 20.1, page 491.
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A non-deterministic Büchi automaton, later referred to just as a Büchi automaton, has a transition function which may have multiple outputs, leading to many possible paths for the same input; it accepts an infinite input if and only if some possible path is accepting. Deterministic and non-deterministic Büchi automata generalize deterministic finite automata and nondeterministic finite automaton to infinite inputs. Each are types of ω-automata. Büchi automata recognize the ω-regular languages, the infinite word version of regular languages.
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The Dancing Links algorithm solving a polycube puzzle In computer science, dancing links is a technique for reverting the operation of deleting a node from a circular doubly linked list. It is particularly useful for efficiently implementing backtracking algorithms, such as Donald Knuth's Algorithm X for the exact cover problem. Algorithm X is a recursive, nondeterministic, depth- first, backtracking algorithm that finds all solutions to the exact cover problem. Some of the better-known exact cover problems include tiling, the n queens problem, and Sudoku.
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Any way you slice them the states are solidly identified and clearly defined. A more featureful event handler is a POE::Session subclass called POE::NFA - an event-driven Nondeterministic finite Automaton (a smarter finite state machine). This event handler moves from one strictly defined state to another as events, polls, user selections, or other external events require. This state machine acts to encapsulate a wide range of generic event driven threads allowing much tighter tracking along the execution path than the relatively informal POE::Session.
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Historically military forces have used the principles of swarming without really examining them explicitly, but there is now active research in consciously examining military doctrines that draw ideas from swarming. In nature and nonmilitary situations, there are other various forms of swarming. Biologically driven forms are often complex adaptive systems, but have no central planning, simple individual rules, and nondeterministic behavior that may or may not evolve with the situation. Current military explorations into swarming address the spectrum of military operations, from strategic through tactical.
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While garbage collection is generally nondeterministic, it is possible to use it in hard real-time systems. A real- time garbage collector should guarantee that even in the worst case it will dedicate a certain number of computational resources to mutator threads. Constraints imposed on a real-time garbage collector are usually either work based or time based. A time based constraint would look like: within each time window of duration T, mutator threads should be allowed to run at least for Tm time.
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The algorithm can be implemented using a pattern matching machine. The algorithm can also be implemented to run on a nondeterministic Turing machine that uses only logarithmic space; the problem of testing unique decipherability is NL-complete, so this space bound is optimal. proves that the complementary problem, of testing for the existence of a string with two decodings, is NL-complete, and therefore that unique decipherability is co-NL-complete. The equivalence of NL-completeness and co-NL-completeness follows from the Immerman–Szelepcsényi theorem.
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A tree automaton is called deterministic (abbreviated DFTA) if no two rules from Δ have the same left hand side; otherwise it is called nondeterministic (NFTA). Non-deterministic top-down tree automata have the same expressive power as non-deterministic bottom-up ones; the transition rules are simply reversed, and the final states become the initial states. In contrast, deterministic top-down tree automataIn a strict sense, deterministic top-down automata are not defined by but they are used there (sect. 1.6, proposition 1.6.
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A deterministic algorithm that performs f(n) steps always finishes in f(n) steps and always returns the same result. A non deterministic algorithm that has f(n) levels might not return the same result on different runs. A non deterministic algorithm may never finish due to the potentially infinite size of the fixed height tree. In computer science, a nondeterministic algorithm is an algorithm that, even for the same input, can exhibit different behaviors on different runs, as opposed to a deterministic algorithm.
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LBT's emphasis on the "willpower muscle" suggests the ability of agency and choice in regard to therapeutic change. Based upon the rejection of a deterministic causative framework in favor of a nondeterministic perspective, LBT maintains compatibility with existentialism and existential psychotherapy. This position of choice is central to existentialist philosopher Jean-Paul Sartre's thinking on human freedom and responsibility, which is one of existential psychotherapist Irvin Yalom's "existential givens". Here, clients are encouraged to confront their inherent freedom by way of choosing how to interpret situations.
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The global state approach was continued in automata theory for finite state machines and push down stack machines including their nondeterministic versions. All of these models have the property of bounded nondeterminism: if a machine always halts when started in its initial state, then there is a bound on the number of states in which it can halt. Hewitt argued that there is a fundamental difference between choices in global state nondeterminism and the arrival order indeterminacy (nondeterminism) of his Actor model. In global state nondeterminism, a "choice" is made for the "next" global state.
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Symmetric Turing machines are a kind of Turing machines with limited nondeterministic power, and were shown to be at least as powerful as deterministic Turing machines, giving an interesting case in between. STIME(T(n)) is the class of the languages accepted by a symmetric Turing machine running in time O(T(n)). It can easily proved that STIME(T)=NTIME(T) by limiting the nondeterminism of any machine in NTIME(T) to an initial stage where a string of symbols is nondeterministically written, followed by deterministic computations.
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If objects are symbols, then their multiplicity within a region matters; however multi-sets are also used in some string models. Regions have associated rules that define how objects are produced, consumed, passed to other regions and otherwise interact with one another. The nondeterministic maximally parallel application of rules throughout the system is a transition between system states, and a sequence of transitions is called a computation. Particular goals can be defined to signify a halting state, at which point the result of the computation would be the objects contained in a particular region.
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Propositional proof systems can be interpreted as nondeterministic algorithms for recognizing tautologies. Proving a superpolynomial lower bound on a proof system P thus rules out the existence of a polynomial-time algorithm for SAT based on P. For example, runs of DPLL algorithm on unsatisfiable instances correspond to tree-like Resolution refutations. Therefore, exponential lower bounds for tree-like Resolution (see below) rule out the existence of efficient DPLL algorithms for SAT. Similarly, exponential Resolution lower bounds imply that SAT solvers based on Resolution, such as CDCL algorithms cannot solve SAT efficiently (in worst-case).
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Walter John Savitch (born February 21, 1943) is best known for defining the complexity class NL (nondeterministic logarithmic space), and for Savitch's theorem, which defines a relationship between the NSPACE and DSPACE complexity classes. His work in establishing complexity classes has helped to create the background against which non-deterministic and probabilistic reasoning can be performed. He has also done extensive work in the field of natural language processing and mathematical linguistics. He has been focused on computational complexity as it applies to genetics and biology for over 10 years.
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Gallier was born January 5, 1949 in Nancy, France, and holds dual French and American citizenship. He earned his baccalauréat at the Lycée de Sèvres in 1966, and a degree in civil engineering at the École Nationale des Ponts et Chaussées in 1972. He then moved to the University of California, Los Angeles for his graduate studies, earning a Ph.D. in computer science in 1978 under the joint supervision of Sheila Greibach and Emily Perlinski Friedman. His dissertation was entitled Semantics and Correctness of Classes of Deterministic and Nondeterministic Recursive Programs.
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Pighizzini obtained optimal state complexity tradeoffs between different types of finite automata over a one-letter alphabet, In particular, in his joint paper with Geffert and Mereghetti he presented the first simulation of two-way nondeterministic finite automata by two-way deterministic finite automata using Savitch's theorem, contributing to the 2DFA vs. 2NFA open question. Jointly with Jirásková, he determined state complexity of self-verifying finite automata. He also contributed to the computational complexity theory by results on sublogarithmic space complexity classes and on the complexity of searching for a lexicographically maximal string.
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In computational complexity theory, the Immerman–Szelepcsényi theorem states that nondeterministic space complexity classes are closed under complementation. It was proven independently by Neil Immerman and Róbert Szelepcsényi in 1987, for which they shared the 1995 Gödel Prize. In its general form the theorem states that NSPACE(s(n)) = co-NSPACE(s(n)) for any function s(n) ≥ log n. The result is equivalently stated as NL = co-NL; although this is the special case when s(n) = log n, it implies the general theorem by a standard padding argument.
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Certain states are defined to be accepting states. An input stream is fed into the machine one character at a time, and the state transitions for the current state are compared to the input stream, and if there is a matching transition the machine may enter a new state. If at the end of the input stream the machine is in an accepting state, then the whole input stream is accepted. ;Nondeterministic finite automaton (NFA): Another simple model of computation, although its processing sequence is not uniquely determined.
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In automata theory and sequential logic, a state-transition table is a table showing what state (or states in the case of a nondeterministic finite automaton) a finite-state machine will move to, based on the current state and other inputs. It is essentially a truth table in which the inputs include the current state along with other inputs, and the outputs include the next state along with other outputs. A state-transition table is one of many ways to specify a finite-state machine. Other ways include a state diagram.
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PDL blends the ideas behind propositional logic and dynamic logic by adding actions while omitting data; hence the terms of PDL are actions and propositions. The TV example above is expressed in PDL whereas the next example involving x:=x+1\,\\! is in first- order DL. PDL is to (first-order) dynamic logic as propositional logic is to first-order logic. Fischer and Ladner showed in their 1977 paper that PDL satisfiability was of computational complexity at most nondeterministic exponential time, and at least deterministic exponential time in the worst case.
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UNITY is a programming language constructed by K. Mani Chandy and Jayadev Misra for their book Parallel Program Design: A Foundation. It is a theoretical language which focuses on what, instead of where, when or how. The language contains no method of flow control, and program statements run in a nondeterministic way until statements cease to cause changes during execution. This allows for programs to run indefinitely, such as auto-pilot or power plant safety systems, as well as programs that would normally terminate (which here converge to a fixed point).
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This definition is the basis for the abbreviation NP; "nondeterministic, polynomial time." These two definitions are equivalent because the algorithm based on the Turing machine consists of two phases, the first of which consists of a guess about the solution, which is generated in a non-deterministic way, while the second phase consists of a deterministic algorithm that verifies if the guess is a solution to the problem.Alsuwaiyel, M. H.: Algorithms: Design Techniques and Analysis, p. 283 Decision problems are assigned complexity classes (such as NP) based on the fastest known algorithms.
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Given a regular expression R, determining whether it generates every string over its alphabet is PSPACE-complete. A related result is that the class of languages recognizable with zero error by automata with two-way infinite random tape equals nondeterministic linear space. This holds for both two-way and multipass one-way access to input. Testing whether an automaton (with two-way infinite random tape) accepts a word with zero error is NSPACE(O(kn)) complete, where n is the input size and k is the number of states.
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Diagram of a counter automaton. Each cell of its stack either contains an "A" or a space symbol. In computer science, more particular in the theory of formal languages, a counter automaton, or counter machine, is a pushdown automaton with only two symbols, A and the initial symbol in \Gamma, the finite set of stack symbols. Equivalently, a counter automaton is a nondeterministic finite automaton with an additional memory cell that can hold one nonnegative integer number (of unlimited size), which can be incremented, decremented, and tested for being zero.
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138) This is indeed the technique by which a deterministic (i.e., a-) Turing machine can be used to mimic the action of a nondeterministic Turing machine; Turing solved the matter in a footnote and appears to dismiss it from further consideration. An oracle machine or o-machine is a Turing a-machine that pauses its computation at state "o" while, to complete its calculation, it "awaits the decision" of "the oracle"—an unspecified entity "apart from saying that it cannot be a machine" (Turing (1939), The Undecidable, p. 166–168).
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Another limitation of Turing machines is that they do not model concurrency well. For example, there is a bound on the size of integer that can be computed by an always-halting nondeterministic Turing machine starting on a blank tape. (See article on unbounded nondeterminism.) By contrast, there are always-halting concurrent systems with no inputs that can compute an integer of unbounded size. (A process can be created with local storage that is initialized with a count of 0 that concurrently sends itself both a stop and a go message.
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Dataflow architecture is a computer architecture that directly contrasts the traditional von Neumann architecture or control flow architecture. Dataflow architectures do not have a program counter (in concept): the executability and execution of instructions is solely determined based on the availability of input arguments to the instructions, so that the order of instruction execution is unpredictable, i.e. behavior is nondeterministic. Although no commercially successful general-purpose computer hardware has used a dataflow architecture, it has been successfully implemented in specialized hardware such as in digital signal processing, network routing, graphics processing, telemetry, and more recently in data warehousing.
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Robinson suggests that the interaction may involve dark energy, dark matter or some other currently unknown scientific process. However, such processes would necessarily be physical, and in this case dualism is replaced with physicalism, or the interaction point is left for study at a later time when these physical processes are understood. Another reply is that the interaction taking place in the human body may not be described by "billiard ball" classical mechanics. If a nondeterministic interpretation of quantum mechanics is correct then microscopic events are indeterminate, where the degree of determinism increases with the scale of the system.
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In their work, Seiden and Woeginger refer to Sylvester's sequence as "Salzer's sequence" after the work of on closest approximation. Znám's problem concerns sets of numbers such that each number in the set divides but is not equal to the product of all the other numbers, plus one. Without the inequality requirement, the values in Sylvester's sequence would solve the problem; with that requirement, it has other solutions derived from recurrences similar to the one defining Sylvester's sequence. Solutions to Znám's problem have applications to the classification of surface singularities (Brenton and Hill 1988) and to the theory of nondeterministic finite automata.
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Algorithm X is the name Donald Knuth gave for "the most obvious trial-and-error approach" for finding all solutions to the exact cover problem. Technically, Algorithm X is a recursive, nondeterministic, depth-first, backtracking algorithm. When Algorithm X is implemented efficiently using Donald Knuth's Dancing Links technique on a computer, Knuth calls it DLX. DLX uses the matrix representation of the problem, implemented as a series of doubly linked lists of the 1s of the matrix: each 1 element has a link to the next 1 above, below, to the left, and to the right of itself.
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As a generalization of pushdown automata, Ginsburg, Greibach, and Harrison (1967) investigated stack automata, which may additionally step left or right in the input string (surrounded by special endmarker symbols to prevent slipping out), and step up or down in the stack in read-only mode. A stack automaton is called nonerasing if it never pops from the stack. The class of languages accepted by nondeterministic, nonerasing stack automata is NSPACE(n2), which is a superset of the context-sensitive languages. The class of languages accepted by deterministic, nonerasing stack automata is DSPACE(n⋅log(n)).
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A major distinction is whether an object's lifetime is deterministic or non-deterministic. This varies by language, and within language varies with the memory allocation of an object; object lifetime may be distinct from variable lifetime. Objects with static memory allocation, notably objects stored in static variables, and classes modules (if classes or modules are themselves objects, and statically allocated), have a subtle non-determinism in many languages: while their lifetime appears to coincide with the run time of the program, the order of creation and destruction – which static object is created first, which second, etc. – is generally nondeterministic.
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If any proof is valid, some path will accept; if no proof is valid, the string is not in the language and it will reject. Conversely, suppose we have a nondeterministic TM called A accepting a given language L. At each of its polynomially many steps, the machine's computation tree branches in at most a finite number of directions. There must be at least one accepting path, and the string describing this path is the proof supplied to the verifier. The verifier can then deterministically simulate A, following only the accepting path, and verifying that it accepts at the end.
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The part of the book on first-order topics ends with a chapter on logical characterizations of resource bounds for parallel random-access machines and circuit complexity. Chapter six introduces Ehrenfeucht–Fraïssé games, a key tool for proving logical inexpressibility, and chapter seven introduces second-order logic. It includes Fagin's theorem characterizing nondeterministic polynomial time in terms of existential second-order logic, the Cook–Levin theorem on the existence of NP-complete problems, and extensions of these results to the polynomial hierarchy. Chapter eight uses games to prove the inexpressibility of certain languages in second- order logic.
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Chapter nine concerns the complementation of languages and the transitive closure operator, including the Immerman–Szelepcsényi theorem that nondeterministic logarithmic space is closed under complementation. Chapter ten provides complete problems and a second-order logical characterization of polynomial space. Chapter eleven concerns uniformity in circuit complexity (the distinction between the existence of circuits for solving a problem, and their algorithmic constructibility), and chapter twelve concerns the role of ordering and counting predicates in logical characterizations of complexity classes. Chapter thirteen uses the switching lemma for lower bounds, and chapter fourteen concerns applications to databases and model checking.
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Even though AFA can accept exactly the regular languages, they are different from other types of finite automata in the succinctness of description, measured by the number of their states. Chandra et al. proved that converting an n-state AFA to an equivalent DFA requires 2^{2^n} states in the worst case. Another construction by Fellah, Jürgensen and Yu. converts an AFA with n states to a nondeterministic finite automaton (NFA) with up to 2^n states by performing a similar kind of powerset construction as used for the transformation of an NFA to a DFA.
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There are at least three different algorithms that decide whether and how a given regex matches a string. The oldest and fastest relies on a result in formal language theory that allows every nondeterministic finite automaton (NFA) to be transformed into a deterministic finite automaton (DFA). The DFA can be constructed explicitly and then run on the resulting input string one symbol at a time. Constructing the DFA for a regular expression of size m has the time and memory cost of O(2m), but it can be run on a string of size n in time O(n).
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He received his BA in Mathematics from the University of California, Berkeley, in 1954. He wrote his Ph.D. thesis on Convergent Sequences of Complete Theories under the supervision of Alonzo Church while at Princeton, and defended his thesis in 1958. Solomon Feferman (2005) writes of this period: After completing his Ph.D. studies, he moved to the University of Chicago, working as an instructor there until 1960. In 1959, he published a joint paper with Michael O. Rabin, a colleague from Princeton, titled Finite Automata and Their Decision Problem (Scott and Rabin 1959) which introduced the idea of nondeterministic machines to automata theory.
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The unrestricted grammars characterize the recursively enumerable languages. This is the same as saying that for every unrestricted grammar G there exists some Turing machine capable of recognizing L(G) and vice versa. Given an unrestricted grammar, such a Turing machine is simple enough to construct, as a two-tape nondeterministic Turing machine. The first tape contains the input word w to be tested, and the second tape is used by the machine to generate sentential forms from G. The Turing machine then does the following: # Start at the left of the second tape and repeatedly choose to move right or select the current position on the tape.
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Spaan et al. [1989] have argued that it is possible for an unboundedly nondeterministic program to solve the halting problem; their algorithm consists of two parts defined as follows: The first part of the program requests a natural number from the second part; after receiving it, it will iterate the desired Turing machine for that many steps, and accept or reject according to whether the machine has yet halted. The second part of the program nondeterministically chooses a natural number on request. The number is stored in a variable which is initialized to 0; then the program repeatedly chooses whether to increment the variable, or service the request.
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These sequences then are the meaning of the program. In the context of functional programs, the final step in a terminating sequence returns the value of the program. (In general there can be many return values for a single program, because the program could be nondeterministic, and even for a deterministic program there can be many computation sequences since the semantics may not specify exactly what sequence of operations arrives at that value.) Perhaps the first formal incarnation of operational semantics was the use of the lambda calculus to define the semantics of LISP. Abstract machines in the tradition of the SECD machine are also closely related.
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SSPACE(S(n)) is the class of the languages accepted by a symmetric Turing machine running in space O(S(n)) and SL=SSPACE(log(n)). SL can equivalently be defined as the class of problems logspace reducible to USTCON. Lewis and Papadimitriou by their definition showed this by constructing a nondeterministic machine for USTCON with properties that they showed are sufficient to make a construction of an equivalent symmetric Turing machine possible. Then, they observed that any language in SL is logspace reducible to USTCON as from the properties of the symmetric computation we can view the special configuration as the undirected edges of the graph.
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In C and C++ programs, a source of particularly difficult-to-diagnose errors is the nondeterministic behavior that results from reading uninitialized variables; this behavior can vary between platforms, builds, and even from run to run. There are two common ways to solve this problem. One is to ensure that all locations are written before they are read. Rice's theorem establishes that this problem cannot be solved in general for all programs; however, it is possible to create a conservative (imprecise) analysis that will accept only programs that satisfy this constraint, while rejecting some correct programs, and definite assignment analysis is such an analysis.
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For a nondeterministic finite automaton A with n states and an m letter alphabet, it is decidable in time O(n2m) whether A is unambiguous. It suffices to use a fixpoint algorithm to compute the set of pairs of states q and q' such that there exists a word w which leads both to q and to q' . The automaton is unambiguous if and only if there is no such a pair such that both states are accepting. There are at most O(n2) state pairs, and for each pair there are m letters to consider to resume the fixpoint algorithm, hence the computation time.
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The map is "a navigational structure which supports the dynamic selection of the intention to be achieved next and the appropriate strategy to achieve it"; it is "a process model in which a nondeterministic ordering of intentions and strategies has been included. It is a labelled directed graph with intentions as nodes and strategies as edges between intentions. The directed nature of the graph shows which intentions can follow which one." The map of the CREWS-L'Ecritoire method looks as follow: Process model of the CREWS-L'Ecritoire method The map consists of goals / intentions (marked with ovals) which are connected by strategies (symbolized through arrows).
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A natural example of a problem in co-RP currently not known to be in P is Polynomial Identity Testing, the problem of deciding whether a given multivariate arithmetic expression over the integers is the zero-polynomial. For instance, is the zero-polynomial while is not. An alternative characterization of RP that is sometimes easier to use is the set of problems recognizable by nondeterministic Turing machines where the machine accepts if and only if at least some constant fraction of the computation paths, independent of the input size, accept. NP on the other hand, needs only one accepting path, which could constitute an exponentially small fraction of the paths.
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Fagin's theorem is the oldest result of descriptive complexity theory, a branch of computational complexity theory that characterizes complexity classes in terms of logic-based descriptions of their problems rather than by the behavior of algorithms for solving those problems. The theorem states that the set of all properties expressible in existential second-order logic is precisely the complexity class NP. It was proven by Ronald Fagin in 1973 in his doctoral thesis, and appears in his 1974 paper. The arity required by the second-order formula was improved (in one direction) in Lynch's theorem, and several results of Grandjean have provided tighter bounds on nondeterministic random-access machines.
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RPDE has the ability to detect subtle changes in natural biological time series such as the breakdown of regular periodic oscillation in abnormal cardiac function which are hard to detect using classical signal processing tools such as the Fourier transform or linear prediction. The recurrence period density is a sparse representation for nonlinear, non-Gaussian and nondeterministic signals, whereas the Fourier transform is only sparse for purely periodic signals. RPDE values H_{norm} for normal sinus rhythm ECG, and for ECG from a patient with sleep apnoea. The time series (plots with blue traces) and spectra (plots with black traces) are relatively difficult to distinguish, nonetheless, the RPDE values are sufficiently different that detection of the abnormality is straightforward.
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The concept of artificial neural network (ANN) was introduced by McCulloch, W. S. & Pitts, W. (1943) for models based on behavior of biological neurons. Norbert Wiener (1961) gave this new field the popular name of cybernetics, whose principle is the interdisciplinary relationship among engineering, biology, control systems, brain functions, and computer science. With the computer science field advancing, the von Neumann-type computer was introduced early in the neuroscience study. But it was not suitable for symbolic processing, nondeterministic computations, dynamic executions, parallel distributed processing, and management of extensive knowledge bases, which are needed for biological neural network applications; and the direction of mind-like machine development changed to a learning machine.
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Euler diagram for P, NP, NP-complete, and NP-hard set of problems. The left side is valid under the assumption that P≠NP, while the right side is valid under the assumption that P=NP (except that the empty language and its complement are never NP-complete, and in general, not every problem in P or NP is NP-complete) In computational complexity theory, a problem is NP-complete when: # A nondeterministic Turing machine can solve it in polynomial-time. # A deterministic Turing machine can solve it in large time complexity classes (e.g., EXPTIME, as is the case with brute force search algorithms) and can verify its solutions in polynomial time.
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Given a regular expression R, if two players take turns playing Ghost with the language generated by R, the problem of determining whether player 1 has a winning strategy is in EXPSPACE, and is PSPACE-hard. It's proved to be PSPACE-hard by reducing Generalized Geography, a problem known to be PSPACE-hard, to a game of Ghost. Specifically, given a Generalized Geography graph, a nondeterministic finite automaton can be constructed, which gives a regular expression R, such that player 1 has a winning strategy in Ghost with R if and only if they have a winning strategy in the Generalized Geography game. This proof extends to Superghost, Superduperghost, Xghost, played on regular languages generated by regular expressions.
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In particular, if the number of public bits shared between Alice and Bob are not counted against the communication complexity, it is easy to argue that computing any function has O(1) communication complexity. On the other hand, both models are equivalent if the number of public bits used by Alice and Bob is counted against the protocol's total communication. Though subtle, lower bounds on this model are extremely strong. More specifically, it is clear that any bound on problems of this class immediately imply equivalent bounds on problems in the deterministic model and the private and public coin models, but such bounds also hold immediately for nondeterministic communication models and quantum communication models.
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However, in some cases a compiler optimization is possible, namely performing escape analysis and proving that escape is not possible, and thus the object can be allocated on the stack; this is significant in Java. In this case object destruction will occur promptly – possibly even during the variable's lifetime (before the end of its scope), if it is unreachable. A complex case is the use of an object pool, where objects may be created ahead of time or reused, and thus apparent creation and destruction may not correspond to actual creation and destruction of an object, only (re)initialization for creation and finalization for destruction. In this case both creation and destruction may be nondeterministic.
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JFLAP (Java Formal Languages and Automata Package) is interactive educational software written in Java for experimenting with topics in the computer science area of formal languages and automata theory, primarily intended for use at the undergraduate level or as an advanced topic for high school. JFLAP allows one to create and simulate structures, such as programming a finite state machine, and experiment with proofs, such as converting a nondeterministic finite automaton (NFA) to a deterministic finite automaton (DFA). JFLAP is developed and maintained at Duke University, with support from the National Science Foundation since 1993. It is freeware and the source code of the most recent version is available, but under some restrictions.
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An important yardstick for describing the relative expressive power of formalisms in this area is the Chomsky hierarchy. It says, for instance, that regular expressions, nondeterministic finite automatons and regular grammars have equal expressive power, while that of context-free grammars is greater; what this means is that the sets of sets of strings described by the first three formalisms are equal, and a proper subset of the set of sets of strings described by context-free grammars. In this area, the cost of expressive power is a central topic of study. It is known, for instance, that deciding whether two arbitrary regular expressions describe the same set of strings is hard, while doing the same for arbitrary context-free grammars is completely impossible.
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Computationally, a context-sensitive language is equivalent to a linear bounded nondeterministic Turing machine, also called a linear bounded automaton. That is a non-deterministic Turing machine with a tape of only kn cells, where n is the size of the input and k is a constant associated with the machine. This means that every formal language that can be decided by such a machine is a context-sensitive language, and every context-sensitive language can be decided by such a machine. This set of languages is also known as NLINSPACE or NSPACE(O(n)), because they can be accepted using linear space on a non-deterministic Turing machine.. The class LINSPACE (or DSPACE(O(n))) is defined the same, except using a deterministic Turing machine.
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The informal term quickly, used above, means the existence of an algorithm solving the task that runs in polynomial time, such that the time to complete the task varies as a polynomial function on the size of the input to the algorithm (as opposed to, say, exponential time). The general class of questions for which some algorithm can provide an answer in polynomial time is called "class P" or just "P". For some questions, there is no known way to find an answer quickly, but if one is provided with information showing what the answer is, it is possible to verify the answer quickly. The class of questions for which an answer can be verified in polynomial time is called NP, which stands for "nondeterministic polynomial time".
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Theorem: An ω-language is recognized by a Büchi automaton if and only if it is an ω-regular language. Proof: Every ω-regular language is recognized by a nondeterministic Büchi automaton; the translation is constructive. Using the closure properties of Büchi automata and structural induction over the definition of ω-regular language, it can be easily shown that a Büchi automaton can be constructed for any given ω-regular language. Conversely, for a given Büchi automaton A = (Q, Σ, Δ, I, F), we construct an ω-regular language and then we will show that this language is recognized by A. For an ω-word w = a1a2... let w(i,j) be the finite segment ai+1...aj-1aj of w.
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NL consists of the decision problems that can be solved by a nondeterministic Turing machine with a read-only input tape and a separate read-write tape whose size is limited to be proportional to the logarithm of the input length. Similarly, L consists of the languages that can be solved by a deterministic Turing machine with the same assumptions about tape length. Because there are only a polynomial number of distinct configurations of these machines, both L and NL are subsets of the class P of deterministic polynomial-time decision problems. Formally, a decision problem is NL-complete when it belongs to NL, and has the additional property that every other decision problem in NL can be reduced to it.
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In addition to Fagin's 1974 paper, Immerman 1999 provides a detailed proof of the theorem. It is straightforward to show that every existential second-order formula can be recognized in NP, by nondeterministically choosing the value of all existentially-qualified variables, so the main part of the proof is to show that every language in NP can be described by an existential second-order formula. To do so, one can use second-order existential quantifiers to arbitrarily choose a computation tableau. In more detail, for every timestep of an execution trace of a non- deterministic Turing machine, this tableau encodes the state of the Turing machine, its position in the tape, the contents of every tape cell, and which nondeterministic choice the machine makes at that step.
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In computational complexity theory, the quantified Boolean formula problem (QBF) is a generalization of the Boolean satisfiability problem in which both existential quantifiers and universal quantifiers can be applied to each variable. Put another way, it asks whether a quantified sentential form over a set of Boolean variables is true or false. For example, the following is an instance of QBF: : \forall x\ \exists y\ \exists z\ ((x \lor z) \land y) QBF is the canonical complete problem for PSPACE, the class of problems solvable by a deterministic or nondeterministic Turing machine in polynomial space and unlimited time. Given the formula in the form of an abstract syntax tree, the problem can be solved easily by a set of mutually recursive procedures which evaluate the formula.
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In this complexity-theoretic context, the vertices of an implicit graph may represent the states of a nondeterministic Turing machine, and the edges may represent possible state transitions, but implicit graphs may also be used to represent many other types of combinatorial structure.. PLS, another complexity class, captures the complexity of finding local optima in an implicit graph.. Implicit graph models have also been used as a form of relativization in order to prove separations between complexity classes that are stronger than the known separations for non-relativized models. For instance, Childs et al. used neighborhood representations of implicit graphs to define a graph traversal problem that can be solved in polynomial time on a quantum computer but that requires exponential time to solve on any classical computer..
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The book has 15 chapters, roughly grouped into five chapters on first-order logic, three on second-order logic, and seven independent chapters on advanced topics. The first two chapters provide background material in first-order logic (including first-order arithmetic, the BIT predicate, and the notion of a first-order query) and complexity theory (including formal languages, resource-bounded complexity classes, and complete problems). Chapter three begins the connection between logic and complexity, with a proof that the first-order-recognizable languages can be recognized in logarithmic space, and the construction of complete languages for logarithmic space, nondeterministic logarithmic space, and polynomial time. The fourth chapter concerns inductive definitions, fixed-point operators, and the characterization of polynomial time in terms of first-order logic with the least fixed-point operator.
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Shortest path algorithms are applied to automatically find directions between physical locations, such as driving directions on web mapping websites like MapQuest or Google Maps. For this application fast specialized algorithms are available. If one represents a nondeterministic abstract machine as a graph where vertices describe states and edges describe possible transitions, shortest path algorithms can be used to find an optimal sequence of choices to reach a certain goal state, or to establish lower bounds on the time needed to reach a given state. For example, if vertices represent the states of a puzzle like a Rubik's Cube and each directed edge corresponds to a single move or turn, shortest path algorithms can be used to find a solution that uses the minimum possible number of moves.
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An ω-language over a finite alphabet Σ is a set of ω-words over Σ, i.e. it is a subset of Σω. An ω-language over Σ is said to be recognized by an ω-automaton A (with the same alphabet) if it is the set of all ω-words accepted by A. The expressive power of a class of ω-automata is measured by the class of all ω-languages that can be recognized by some automaton in the class. The nondeterministic Büchi, parity, Rabin, Streett, and Muller automata, respectively, all recognize exactly the same class of ω-languages.. These are known as the ω-Kleene closure of the regular languages or as the regular ω-languages. Using different proofs it can also be shown that the deterministic parity, Rabin, Streett, and Muller automata all recognize the regular ω-languages.
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Holland thus argues that both the biological theory and the biological evidence is nondeterministic and nonreductive, and that biology as a theoretical and empirical endeavor (as opposed to 'biology' as a cultural-symbolic nexus as outlined in Schneider's 1968 book) actually supports the nurture kinship perspective of cultural anthropologists working post-Schneider (see above sections). Holland argues that, whilst there is nonreductive compatibility around human kinship between anthropology, biology and psychology, for a full account of kinship in any particular human culture, ethnographic methods, including accounts of the people themselves, the analysis of historical contingencies, symbolic systems, economic and other cultural influences, remain centrally important. Holland's position is widely supported by both cultural anthropologists and biologists as an approach which, according to Robin Fox, "gets to the heart of the matter concerning the contentious relationship between kinship categories, genetic relatedness and the prediction of behavior".
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The butterfly network, a multitree used in distributed computation, showing the subtree reachable from one of its vertices. In combinatorics and order- theoretic mathematics, a multitree may describe either of two equivalent structures: a directed acyclic graph (DAG) in which the set of vertices reachable from any vertex induces a tree, or a partially ordered set (poset) that does not have four items a, b, c, and d forming a diamond suborder with and but with b and c incomparable to each other (also called a diamond-free poset.). In computational complexity theory, multitrees have also been called strongly unambiguous graphs or mangroves; they can be used to model nondeterministic algorithms in which there is at most one computational path connecting any two states.. Multitrees may be used to represent multiple overlapping taxonomies over the same ground set.. If a family tree may contain multiple marriages from one family to another, but does not contain marriages between any two blood relatives, then it forms a multitree..
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Similarly, if one thread reads from a location while another thread is writing to it, it may be possible for the read to return a value that is some arbitrary and meaningless combination of the bits representing the value that the memory location held before the write, and of the bits representing the value being written. On many platforms, special memory operations are provided for simultaneous access; in such cases, typically simultaneous access using these special operations is safe, but simultaneous access using other memory operations is dangerous. Sometimes such special operations (which are safe for simultaneous access) are called atomic or synchronization operations, whereas the ordinary operations (which are unsafe for simultaneous access) are called data operations. This is probably why the term is data race; on many platforms, where there is a race condition involving only synchronization operations, such a race may be nondeterministic but otherwise safe; but a data race could lead to memory corruption or undefined behavior.
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However, a procedure to apply any simple function over the whole list, in other words , is straight- forward: (map φ) xlist = [ φ(x1), φ(x2), ..., φ(xn) ] Now, these two procedures already promote `List` to an applicative functor. To fully qualify as a monad, only a correct notion of to flatten repeated structure is needed, but for lists, that just means unwrapping an outer list to append the inner ones that contain values: join(xlistlist) = join([xlist1, xlist2, ..., xlistn]) = xlist1 ++ xlist2 ++ ... ++ xlistn The resulting monad is not only a list, but one that automatically resizes and condenses itself as functions are applied. can now also be derived with just a formula, then used to feed `List` values through a pipeline of monadic functions: (xlist >>= f) = join ∘ (map f) xlist One application for this monadic list is representing nondeterministic computation. `List` can hold results for all execution paths in an algorithm, then condense itself at each step to "forget" which paths led to which results (a sometimes important distinction from deterministic, exhaustive algorithms).
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More specifically, define the Hajós number of a -chromatic graph to be the minimum number of steps needed to construct from , where each step forms a new graph by combining two previously formed graphs, merging two nonadjacent vertices of a previously formed graph, or adding a vertex or edge to a previously formed graph. They showed that, for an -vertex graph with edges, . If every graph has a polynomial Hajós number, this would imply that it is possible to prove non-colorability in nondeterministic polynomial time, and therefore imply that NP = co-NP, a conclusion considered unlikely by complexity theorists.. However, it is not known how to prove non-polynomial lower bounds on the Hajós number without making some complexity-theoretic assumption, and if such a bound could be proven it would also imply the existence of non-polynomial bounds on certain types of Frege system in mathematical logic. The minimum size of an expression tree describing a Hajós construction for a given graph may be significantly larger than the Hajós number of , because a shortest expression for may re-use the same graphs multiple times, an economy not permitted in an expression tree.
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