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unsolvable problem

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  • 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

  • Word problem for groups — In mathematics, especially in the area of abstract algebra known as combinatorial group theory, the word problem for a recursively presented group G is the algorithmic problem of deciding whether two words represent the same element. Although it… …   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

  • Hilbert's tenth problem — is the tenth on the list of Hilbert s problems of 1900. Its statement is as follows:Given a Diophantine equation with any number of unknown quantities and with rational integral numerical coefficients: To devise a process according to which it… …   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

  • Znám's problem — In number theory, Znám s problem asks which sets of k integers have the property that each integer in the set is a proper divisor of the product of the other integers in the set, plus 1. Znám s problem is named after the Slovak mathematician… …   Wikipedia

  • 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

  • Constant problem — In mathematics, the constant problem is the problem of deciding if a given expression is equal to zero. Contents 1 The problem 2 Results 3 See also 4 References …   Wikipedia

  • Grand Challenge problem — A Grand Challenge Problem is a general category of unsolved problems. The definition of a Grand Challenge problem has a certain degree of inherent subjectivity surrounding what is, or is not, a Grand Challenge. A Grand Challenge problem exhibits… …   Wikipedia

  • History of the Church–Turing thesis — This article is an extension of the history of the Church–Turing thesis. The debate and discovery of the meaning of computation and recursion has been long and contentious. This article provides detail of that debate and discovery from Peano s… …   Wikipedia

  • History of the Church-Turing thesis — This article is an extension of the history of the Church Turing thesis.The debate and discovery of the meaning of computation and recursion has been long and contentious. This article provides detail of that debate and discovery from Peano s… …   Wikipedia

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