Undecidability of the Regularity Problem for Turing Machines (REGULARTM )
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Introduction & Overview
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Quick Overview
The **Regularity Problem for Turing Machines (REGULARTM)** asks if the language accepted by a given Turing Machine (M) is a regular language. This problem is **undecidable**. Its undecidability is proven by a many-one reduction from the Halting Problem (HALTTM). A reduction function takes an instance of HALTTM (\) and constructs a new TM, M\_prime. M\_prime is designed to accept a non-regular language (e.g., {0^n 1^n}) if M\_halting does not halt on w, and to accept a regular language (e.g., Sigma\*) if M\_halting halts on w. Since deciding if L(M\_prime) is regular would allow us to solve the Halting Problem, REGULARTM must be undecidable.