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

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...

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

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

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...

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

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

order Horn clauses. 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...

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...

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...

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

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...

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

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...

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...

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...

them. The halting problem is an important undecidable decision problem; for more examples, see list of undecidable problems. Decision problems can be ordered...

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

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...

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...

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

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...

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...

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...

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

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

types. The halting problem is not in ExpGenP for any model of Turing machine, The Post correspondence problem is in ExpGenP. The decision problem for Presburger...