Definition: A problem that cannot be solved for all cases by any algorithm whatsoever---equivalently, whose associated language cannot be recognized by a Turing machine that halts for all inputs.
Specialization (... is a kind of me.)
halting problem, Post's correspondence problem.
See also decidable problem, unsolvable problem, undecidable language, intractable, busy beaver.
Note: From Algorithms and Theory of Computation Handbook, page 24-19 or 26-20, Copyright © 1999 by CRC Press LLC. Appearing in the Dictionary of Computer Science, Engineering and Technology, Copyright © 2000 CRC Press LLC.
If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.
Entry modified 9 August 2004.
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Cite this as:
Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "undecidable problem", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology. 9 August 2004. (accessed TODAY) Available from: http://www.nist.gov/dads/HTML/undecidableProblem.html