Well, the researchers use the word "incomputable" in their paper, posted on the ArXiv preprint server, which in the world of theoretical computer science is perhaps even more damning.
|
|
It follows that the original "no free lunch" theorem does not apply to what can be stored in a physical computer; instead the so-called "tightened" no free lunch theorems need to be applied. It has also been shown that NFL results apply to incomputable functions .
|
|
Algorithmic Probability is the only probability system known to be complete in this way. As a necessary consequence of its completeness it is incomputable. The incomputability is because some algorithms—a subset of those that are partially recursive—can never be evaluated fully because it would take too long. But these programs will at least be recognized as possible solutions.
|
|
Like Solomonoff induction, AIXI is incomputable. However, there are computable approximations of it. One such approximation is AIXItl, which performs at least as well as the provably best time t and space l limited agent. Another approximation to AIXI with a restricted environment class is MC-AIXI (FAC-CTW) (which stands for Monte Carlo AIXI FAC-Context-Tree Weighting), which has had some success playing simple games such as partially observable Pac-Man.
|
|
This has been termed the strong Church–Turing thesis, or Church–Turing–Deutsch principle, and is a foundation of digital physics. #The universe is not equivalent to a Turing machine (i.e., the laws of physics are not Turing-computable), but incomputable physical events are not "harnessable" for the construction of a hypercomputer. For example, a universe in which physics involves random real numbers, as opposed to computable reals, would fall into this category.
|
|
Within the constraints that the graph goes down at an angle of at least 45 degrees, that it starts at n and ends approximately at K(x), every graph (up to a O(\log n) additive term in argument and value) is realized by the structure function of some data x and vice versa. Where the graph hits the diagonal first the argument (complexity) is that of the minimum sufficient statistic. It is incomputable to determine this place. See.
|
|
The origin of countless conspiracy theories Cristian S. Calude stated that: "given the impossibility of true randomness, the effort is directed towards studying degrees of randomness".Cristian S. Calude, (2017). "Quantum Randomness: From Practice to Theory and Back" in "The Incomputable Journeys Beyond the Turing Barrier" Editors: S. Barry Cooper, Mariya I. Soskova, 169–181, doi:10.1007/978-3-319-43669-2_11. It can be proven that there is infinite hierarchy (in terms of quality or strength) of forms of randomness.
|
|
The use of well-established zero-knowledge proof primitives such as Schnorr's scheme greatly simplifies the security proofs. Given that the underlying zero knowledge proof primitive is secure, the YAK protocol aims to satisfy the following properties. # Private key security – An attacker cannot learn the user's static private key even if he is able to learn all session- specific secrets in any compromised session. # Forward secrecy – Session keys that were securely established in the past uncorrupted sessions will remain incomputable in the future even when both users' static private keys are disclosed.
|
|
The algorithmic probability of any given finite output prefix q is the sum of the probabilities of the programs that compute something starting with q. Certain long objects with short programs have high probability. Algorithmic probability is the main ingredient of Solomonoff's theory of inductive inference, the theory of prediction based on observations; it was invented with the goal of using it for machine learning; given a sequence of symbols, which one will come next? Solomonoff's theory provides an answer that is optimal in a certain sense, although it is incomputable.
|
|
In his report, he published the proof for the convergence theorem. In the years following his discovery of Algorithmic Probability he focused on how to use this probability and Solomonoff Induction in actual prediction and problem solving for A.I. He also wanted to understand the deeper implications of this probability system. One important aspect of Algorithmic Probability is that it is complete and incomputable. In the 1968 report he shows that Algorithmic Probability is complete; that is, if there is any describable regularity in a body of data, Algorithmic Probability will eventually discover that regularity, requiring a relatively small sample of that data.
|
|
This often presents challenges to optimizing compilers, which must have a great amount of knowledge of the specific CPU and other hardware available on the compilation target to best optimize a program for performance. In the extreme case, a compiler may be forced to emulate instructions not supported on a compilation target platform, forcing it to generate code or link an external library call to produce a result that is otherwise incomputable on that platform, even if it is natively supported and more efficient in hardware on other platforms. This is often the case in embedded systems with respect to floating-point arithmetic, where small and low-power microcontrollers often lack hardware support for floating- point arithmetic and thus require computationally expensive software routines to produce floating point calculations.
|
|
Circular references also occur in spreadsheets when two cells require each other's result. For example, if the value in Cell A1 is to be obtained by adding 5 to the value in Cell B1, and the value in Cell B1 is to be obtained by adding 3 to the value in Cell A1, no values can be computed. (Even if the specifications are A1:=B1+5 and B1:=A1-5, there is still a circular reference. It does not help that, for instance, A1=3 and B1=-2 would satisfy both formulae, as there are infinitely many other possible values of A1 and B1 that can satisfy both instances.) Circular reference in worksheets can be a very useful technique for solving implicit equations such as the Colebrook equation and many others, which might otherwise require tedious Newton-Raphson algorithms in VBA or use of macros.. A distinction should be made with processes containing a circular reference between those that are incomputable and those that are an iterative calculation with a final output.
|
|