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- Undecidable_problem abstract "In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is known to be impossible to construct a single algorithm that always leads to a correct yes-or-no answer.A decision problem is any arbitrary yes-or-no question on an infinite set of inputs. Because of this, it is traditional to define the decision problem equivalently as the set of inputs for which the problem returns yes. These inputs can be natural numbers, but also other values of some other kind, such as strings of a formal language. Using some encoding, such as a Gödel numbering, the strings can be encoded as natural numbers. Thus, a decision problem informally phrased in terms of a formal language is also equivalent to a set of natural numbers. To keep the formal definition simple, it is phrased in terms of subsets of the natural numbers.Formally, a decision problem is a subset of the natural numbers. The corresponding informal problem is that of deciding whether a given number is in the set. A decision problem A is called decidable or effectively solvable if A is a recursive set. A problem is called partially decidable, semi-decidable, solvable, or provable if A is a recursively enumerable set. This means that there exists an algorithm that halts eventually when the answer is yes but may run for ever if the answer is no. Partially decidable problems and any other problems that are not decidable are called undecidable.".
- Undecidable_problem wikiPageID "15631055".
- Undecidable_problem wikiPageRevisionID "594020117".
- Undecidable_problem hasPhotoCollection Undecidable_problem.
- Undecidable_problem subject Category:Formal_theories_of_arithmetic.
- Undecidable_problem subject Category:Logic_in_computer_science.
- Undecidable_problem subject Category:Model_theory.
- Undecidable_problem subject Category:Proof_theory.
- Undecidable_problem type Abstraction100002137.
- Undecidable_problem type Cognition100023271.
- Undecidable_problem type Explanation105793000.
- Undecidable_problem type FormalTheoriesOfArithmetic.
- Undecidable_problem type HigherCognitiveProcess105770664.
- Undecidable_problem type Process105701363.
- Undecidable_problem type PsychologicalFeature100023100.
- Undecidable_problem type Theory105989479.
- Undecidable_problem type Thinking105770926.
- Undecidable_problem comment "In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is known to be impossible to construct a single algorithm that always leads to a correct yes-or-no answer.A decision problem is any arbitrary yes-or-no question on an infinite set of inputs. Because of this, it is traditional to define the decision problem equivalently as the set of inputs for which the problem returns yes.".
- Undecidable_problem label "Problem nierozstrzygalny".
- Undecidable_problem label "Problema indecidible".
- Undecidable_problem label "Problema indecidível".
- Undecidable_problem label "Undecidable problem".
- Undecidable_problem label "Алгоритмически неразрешимая задача".
- Undecidable_problem label "معضلة غير قابلة للقرار".
- Undecidable_problem sameAs Problema_indecidible.
- Undecidable_problem sameAs Problem_nierozstrzygalny.
- Undecidable_problem sameAs Problema_indecidível.
- Undecidable_problem sameAs m.03nn3tw.
- Undecidable_problem sameAs Q3502995.
- Undecidable_problem sameAs Q3502995.
- Undecidable_problem sameAs Undecidable_problem.
- Undecidable_problem wasDerivedFrom Undecidable_problem?oldid=594020117.
- Undecidable_problem isPrimaryTopicOf Undecidable_problem.