GATE CSE
First time here? Checkout the FAQ!
x
0 votes
40 views
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 (50k points)   | 40 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.

1 Answer

0 votes
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 (1.1k points)  
Top Users Jan 2017
  1. Debashish Deka

    9872 Points

  2. sudsho

    5596 Points

  3. Habibkhan

    5498 Points

  4. Bikram

    5350 Points

  5. Vijay Thakur

    4508 Points

  6. Arjun

    4458 Points

  7. Sushant Gokhale

    4410 Points

  8. saurabh rai

    4236 Points

  9. santhoshdevulapally

    3906 Points

  10. Kapil

    3892 Points

Monthly Topper: Rs. 500 gift card

19,481 questions
24,261 answers
54,211 comments
20,405 users