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Choose the correct alternatives (more than one may be correct) and write the corresponding letters only: Which of the following is the strongest correct statement about a finite language over some finite alphabet  ?
  • a)
    It could be undecidable
  • b)
    It is Turing-machine recognizable
  • c)
    It is a context sensitive language.
  • d)
    It is a regular language.
  • e)
    None of the above,
Correct answer is option 'B,C,D'. Can you explain this answer?
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Choose the correct alternatives (more than one may be correct) and wri...
Explanation:

  • Option A: A finite language over some finite alphabet can never be undecidable as it can be recognized by a Turing machine which is a decider.

  • Option B: A finite language over some finite alphabet is Turing-machine recognizable as we can construct a Turing machine that accepts every string in the language and rejects every string not in the language.

  • Option C: A finite language over some finite alphabet can be a context-sensitive language, but it is not always the case. It depends on the grammar of the language.

  • Option D: A finite language over some finite alphabet is always a regular language as it can be recognized by a finite automaton which is a regular language recognizer.

  • Option E: None of the above options are completely correct. Options B, C, and D are correct statements about a finite language over some finite alphabet.

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Choose the correct alternatives (more than one may be correct) and wri...
(b), (c) and (d) are true. But the strongest answer would be (d) a regular language. It is trivial to say that a finite set of strings (finite language) can be accepted using a finite set of states. And regular language ⊂ context-free ⊂ contextsensitive ⊂ Turing recognizable, would imply that regular language is the strongest answer. 
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