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In computability theory, an undecidable problem is a decision problem for which an effective method (algorithm) to derive the correct answer does not exist. More formally, an undecidable problem is a problem whose language is not a recursive set; see the article Decidable language.
In planning and policy, a wicked problem is a problem that is difficult or impossible to solve because of incomplete, contradictory, and changing requirements that are often difficult to recognize.
A mathematical problem is a problem that can be 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 problem of a more abstract nature, such as Hilbert's problems.
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"Undecidable", sometimes also used as a synonym of independent, something that can neither be proved nor disproved within a mathematical theory Undecidable figure , a two-dimensional drawing of something that cannot exist in 3d, such as appeared in some of the works of M. C. Escher
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Matiyasevich showed this problem to be unsolvable by mapping a Diophantine equation to a recursively enumerable set and invoking Gödel's Incompleteness Theorem. [5] In 1936, Alan Turing proved that the halting problem—the question of whether or not a Turing machine halts on a given program—is undecidable, in the second sense of the term.
1957 () – 1958 (): John Britton gives another proof that the word problem for groups is unsolvable, based on Turing's cancellation semigroups result and some of Britton's earlier work. [20] An early version of Britton's Lemma appears. [3]: 355 1958 () – 1959 (): Boone publishes a simplified version of his construction.