In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the...

for every program. The theorem generalizes the undecidability of the halting problem. It has far-reaching implications on the feasibility of static analysis...

one could calculate the halting problem for all programs of a size up to N. Let the program p for which the halting problem is to be solved be N bits...

that the halting problem is NP-hard but not NP-complete. For example, the Boolean satisfiability problem can be reduced to the halting problem by transforming...

an algorithm that always leads to a correct yes-or-no answer. The halting problem is an example: it can be proven that there is no algorithm that correctly...

computable function. This has implications in computability theory, the halting problem, and complexity theory. The concept of a busy beaver was first introduced...

is not recursive. The halting problem is therefore called non-computable or undecidable. An extension of the halting problem is called Rice's theorem...

include the limits of knowledge, ignorabimus, unknown unknowns, the halting problem, and chaos theory. Nicholas Rescher provides the most recent focused...

undecidable in ZFC. The halting problem (determining whether a Turing machine halts on a given input) and the mortality problem (determining whether it...

Cantor's diagonal argument, Gödel's incompleteness theorem, and Turing's halting problem. In particular, no program P computing a lower bound for each text's...

accordingly. Some of the most important problems in mathematics are undecidable, e.g. the halting problem. The field of computational complexity theory...

problem can be of any complexity class. Even undecidable problems, such as the halting problem, can be used. An oracle machine can be conceived as a Turing...

the terminology. Not every set of natural numbers is computable. The halting problem, which is the set of (descriptions of) Turing machines that halt on...

not Turing-computable. For example, a machine that could solve the halting problem would be a hypercomputer; so too would one that could correctly evaluate...

^{2}t)} time. This version of the halting problem is among the simplest, most-easily described undecidable decision problems: Given an arbitrary positive integer...

decision problem is undecidable. However, that there is some Turing machine with undecidable halting problem means that the halting problem for a universal...

Hence, the problem is known to need more than exponential run time. Even more difficult are the undecidable problems, such as the halting problem. They cannot...

correspondence problem is an undecidable decision problem that was introduced by Emil Post in 1946. Because it is simpler than the halting problem and the...

proof (termination proof) can never be fully automated, since the halting problem is undecidable. For example, successively searching through integers...

proved that the problem Given g and n, does the sequence of iterates gk(n) reach 1? is undecidable, by representing the halting problem in this way. Closer...

termination analysis utilizes this principle in order to solve the universal halting problem for a certain class of programs. When applied to general programs,...

factors of n. An example of a computational problem without a solution is the Halting problem. Computational problems are one of the main objects of study in...

whether M will eventually produce s. This is due to the fact that the halting problem is unsolvable, which has major implications for the theoretical limits...

unsolvable, and Turing's theorem that there is no algorithm to solve the halting problem. The incompleteness theorems apply to formal systems that are of sufficient...

method' which decides whether any given Turing machine halts or not (the halting problem). If 'algorithm' is understood as meaning a method that can be represented...

are so-called undecidable problems, such as the halting problem for Turing machines. Some well-known difficult abstract problems that have been solved relatively...

Gödel's first incompleteness theorem Tarski's undefinability theorem Halting problem Kleene's recursion theorem Diagonalization (disambiguation) This disambiguation...

determining whether it is a decider is an undecidable problem. This is a variant of the halting problem, which asks for whether a Turing machine halts on...

whether a computer program contains an infinite loop or not; this is the halting problem. This differs from "a type of computer program that runs the same instructions...

well-defined characterisation under this definition. This includes the halting problem and the busy beaver game. It remains an open question as to whether...