Intermediate
Theoretical Undecidability of the Halting Problem
Investigate the proof that it is impossible to decide algorithmically whether a given program will finish running or continue forever.
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Describe the theoretical proof of the undecidability of the Halting Problem using a diagonalization argument or a self-reference paradox. Explain the definition of a 'decider' and why assuming the existence of a halting decider leads to a logical contradiction, thereby establishing the limits of computation.