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Which among the following is true for the given statement?Statement :If there are strings R and T in a language L so that R is prefix of T and R is not equivalent to T.
  • a)
    No DPDA can accept L by empty stack
  • b)
    DPDA can accept L by an empty stack
  • c)
    L is regular
  • d)
    None of the mentioned
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Which among the following is true for the given statement?Statement :I...
If M is a DPDA accepting L by an empty stsck, R and T are distinct strings in L, and R is a prefix of T, then the sequence of moves M must make in order to accept R leaves the stack empty, since R∈L. But then T cannot be accepted, since M cant move with an empty stack.
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Most Upvoted Answer
Which among the following is true for the given statement?Statement :I...
Explanation:

The given statement states that there are two strings R and T in a language L such that R is a prefix of T and R is not equivalent to T. Let's analyze the options given:

a) No DPDA can accept L by empty stack: This option is true because if R is a prefix of T and R is not equivalent to T, then there exist some strings in L that have the same prefix as R but do not match T. This means that the DPDA cannot determine when to pop the stack and accept the string. Therefore, no DPDA can accept L by an empty stack.

b) DPDA can accept L by an empty stack: This option is false because of the reason mentioned above.

c) L is regular: This option may or may not be true as the given information is not sufficient to determine the regularity of L.

d) None of the mentioned: This option is false as option a is true.

Therefore, option a is the correct answer.

HTML Representation:

Explanation:

The given statement states that there are two strings R and T in a language L such that R is a prefix of T and R is not equivalent to T. Let's analyze the options given:


  • a) No DPDA can accept L by empty stack: This option is true because if R is a prefix of T and R is not equivalent to T, then there exist some strings in L that have the same prefix as R but do not match T. This means that the DPDA cannot determine when to pop the stack and accept the string. Therefore, no DPDA can accept L by an empty stack.

  • b) DPDA can accept L by an empty stack: This option is false because of the reason mentioned above.

  • c) L is regular: This option may or may not be true as the given information is not sufficient to determine the regularity of L.

  • d) None of the mentioned: This option is false as option a is true.


Therefore, option a is the correct answer.
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