halting problem

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halting problem
The fundamental decision problem in the theory of computation. It is the problem of finding whether there is an effective procedure for telling whether a Turing machine computation ever terminates, for an arbitrary input. The negative solution is that there is no such procedure. So there can be no ‘program tester’ that, given any program and its input, answers the question of whether the program ever terminates.

Philosophy dictionary. . 2011.

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