Assuming the Church–Turing thesis, the halting problem is algorithmically unsolvable or undecidable. It is one example of many unsolvable problems in mathematics and computer science. It has profound practical implications: if it were solvable it would be possible to write a program tester that, given (say) any Pascal program and its input, would print “yes” if the program terminated after a finite number of steps and “no” if it did not. For any programming language that can define the recursive functions, no such termination program exists.
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