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undecidable problem

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  • 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

  • Undecidable — has more than one meaning:;In mathematical logic: * A decision problem is called (recursively) undecidable if no algorithm can decide it, such as for Turing s halting problem; see also under Decidable and Undecidable problem. * Undecidable is… …   Wikipedia

  • 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

  • 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

  • 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

  • List of undecidable problems — In computability theory, an undecidable problem is a problem whose language is not a recursive set. More informally, such problems cannot be solved in general by computers; see decidability. This is a list of undecidable problems. Note that there …   Wikipedia

  • Whitehead problem — In group theory, a branch of abstract algebra, the Whitehead problem is the following question::Is every abelian group A with Ext1( A , Z) = 0 a free abelian group?Abelian groups satisfying this condition are sometimes called Whitehead groups, so …   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

  • List of statements undecidable in ZFC — The following is a list of mathematical statements that are undecidable in ZFC (the Zermelo–Fraenkel axioms plus the axiom of choice), assuming that ZFC is consistent.Functional analysisCharles Akemann and Nik Weaver showed in 2003 that the… …   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

  • Domino problem — An aperiodic set of Wang dominoes.[1] In geometry, the domino problem is the problem of deciding whether a set of tiles of a particular kind admits a tiling. In a 1961 paper[2] …   Wikipedia

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