halting problem
The fundamental decision problem in the theory of computation. It is the problem of finding whether there is an effective procedure for telling whether a Turing machine computation ever terminates, for an arbitrary input. The negative solution is that there is no such procedure. So there can be no ‘program tester’ that, given any program and its input, answers the question of whether the program ever terminates.

Philosophy dictionary. . 2011.

Look at other dictionaries:

  • Halting problem — In computability theory, the halting problem can be stated as follows: Given a description of a computer program, decide whether the program finishes running or continues to run forever. This is equivalent to the problem of deciding, given a… …   Wikipedia

  • halting problem — noun The problem of deciding in finite time whether any program will finish running in finite time, when given a certain finite input …   Wiktionary

  • Halting problem — …   Википедия

  • Undecidable problem — In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is impossible to construct an algorithm that leads to a yes or no answer the problem is not decidable.A decision problem is any …   Wikipedia

  • Decision problem — A decision problem has only two possible outputs, yes or no (or alternately 1 or 0) on any input. In computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes or no answer,… …   Wikipedia

  • P versus NP problem — Unsolved problems in computer science Is P = NP ? …   Wikipedia

  • P = NP problem — The relationship between the complexity classes P and NP is an unsolved question in theoretical computer science. It is considered to be the most important problem in the field – the Clay Mathematics Institute has offered a $1 million US prize… …   Wikipedia

  • Post correspondence problem — The Post correspondence problem is an undecidable decision problem that was introduced by Emil Post in 1946.[1] Because it is simpler than the halting problem and the Entscheidungsproblem it is often used in proofs of undecidability. Contents 1… …   Wikipedia

  • Mathematical problem — A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real world problem, such as computing the orbits of the planets in the solar system, or a… …   Wikipedia

  • Chaitin's constant — In the computer science subfield of algorithmic information theory, a Chaitin constant or halting probability is a real number that informally represents the probability that a randomly constructed program will halt. These numbers are formed from …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”