The Undecidable Problem in Computability Theory
In computability theory, the halting problem is a decision problem which can be stated as follows:
- Given the description of an arbitrary program and a finite input, decide whether the program finishes running or will run forever.
Alan Turing proved in 1936 that a general algorithm running on a Turing machine that solves the halting problem for all possible program-input pairs necessarily cannot exist. Hence, the halting problem is undecidable for Turing machines.
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