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Entscheidungsproblem
In mathematics, the Entscheidungsproblem (German for 'decision problem') is a challenge posed by David Hilbert in 1928. The Entscheidungsproblem asks for a computer program that will take as input a description of a formal language and a mathematical statement in the language and return as output either "True" or "False" according to whether the statement is true or false. The program need not justify its answer, or provide a proof, so long as it is always correct. Such a computer program would be able to decide, for example, whether statements such as the continuum hypothesis or the Riemann hypothesis are true, even though no proof or disproof of these statements is known. The Entscheidungsproblem has often been identified in particular with the decision problem for first-order logic (that is, the problem of algorithmically determining whether a first-order statement is universally valid).
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