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Consider the following statements about a TM that accepts a language L:
S1: If the string in the language L, then TM halts in final state.
S2: If the string not in the language L, then TM may halt in non-final state or never halt.
If the string given as an input to the TM, then which of the above statements are correct?
  • a)
     S1 only
  • b)
     S2 only
  • c)
     Data inadequate
  • d)
     None of these
Correct answer is option 'A,B'. Can you explain this answer?
Most Upvoted Answer
Consider the following statements about a TM that accepts a language L...
Answer:

Let's analyze each statement separately:

S1: If the string is in the language L, then TM halts in a final state.
This statement is correct. If the string is in the language L, it means that the Turing Machine recognizes and accepts it. In this case, the Turing Machine will eventually reach a final state and halt.

S2: If the string is not in the language L, then TM may halt in a non-final state or never halt.
This statement is also correct. If the string is not in the language L, it means that the Turing Machine does not recognize it. In this case, there are two possibilities:
1. The Turing Machine may reach a non-final state and halt. This can happen if the Turing Machine encounters a configuration that leads to a non-final state.
2. The Turing Machine may never halt. This can happen if the Turing Machine enters into an infinite loop, continuously transitioning between different states without reaching a final or non-final state.

Conclusion:
Both statements S1 and S2 are correct. If the string is in the language L, the Turing Machine will halt in a final state. If the string is not in the language L, the Turing Machine may halt in a non-final state or never halt.
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Community Answer
Consider the following statements about a TM that accepts a language L...
Both statements S1 and S2 are true for TM. TM always halts in the final state if the given input string is valid, otherwise, it may halt in the non-final state or never halts.
Hence, the correct options are (A) and (B).
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Consider the following statements about a TM that accepts a language L:S1: If the string in the language L, then TM halts in final state.S2: If the string not in the language L, then TM may halt in non-final state or never halt.If the string given as an input to the TM, then which of the above statements are correct?a)S1 onlyb)S2 onlyc)Data inadequated)None of theseCorrect answer is option 'A,B'. Can you explain this answer?
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