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Let A = {<M>|M is a TM and L(M) is regular}. Then A is _________

a) Decidable language and regular language

b) Undecidable but partially decidable

c) Totally not decidable

d) Decidable language but not regular language
asked in Theory of Computation by Veteran (53.1k points)   | 80 views
I think C, since we can take one Tyes = a and Tno = a^nb^n .Then Tyes subset of Tno.Hence not even R.E.

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Option B. According to Rice's theorem, anything non-trivial is undecidable. This is partially decidable, suppose the TM accepts a regular language, we can test this by passing all regular strings one after another, sooner or later the TM is going to stop by accepting it because it accepts reg language. This process can be fastened by using dovetailing technique i.e processing n strings parallely. But suppose the given TM doesn't accept regular language then the TM would be running forever checking every regular string. Thus it is partially decidable.
answered by Active (1.2k points)  

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