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.