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Which of the following can be accepted by a DPDA?
- a)The set of even length palindrome over {a,b}
- b)The set of odd length palindrome over {a,b}
- c){xxc| where c stands for the complement,{0,1}}
- d)None of the mentioned
Correct answer is option 'D'. Can you explain this answer?
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Which of the following can be accepted by a DPDA?a)The set of even len...
Theorem: The language pal of palindromes over the alphabet {0,1} cannot be accepted by any finite automaton , and it is therefore not regular.
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Which of the following can be accepted by a DPDA?a)The set of even len...
Explanation:
A Deterministic Pushdown Automaton (DPDA) is a finite-state machine with a stack that can read input symbols, push or pop symbols from the stack, and transition between states based on the current input symbol and stack symbol.
In order for a string to be accepted by a DPDA, it must follow certain rules and satisfy specific conditions. Let's analyze each of the given options to determine whether they can be accepted by a DPDA.
a) The set of even length palindrome over {a,b}
A palindrome is a string that reads the same forwards and backwards. In this case, we are considering palindromes of even length over the alphabet {a,b}. Since a DPDA has a finite stack, it cannot keep track of an arbitrary number of symbols to ensure that the string is a palindrome. Therefore, a DPDA cannot accept this language.
b) The set of odd length palindrome over {a,b}
Similarly, this language consists of odd length palindromes over the alphabet {a,b}. Again, a DPDA cannot keep track of an arbitrary number of symbols to ensure that the string is a palindrome. Hence, a DPDA cannot accept this language either.
c) {xxc| where c stands for the complement,{0,1}}
This language consists of strings of the form "xxc" where c is the complement of x. The complement of x can be either '0' or '1'. This language can be accepted by a DPDA. The DPDA can read the first 'x', push it onto the stack, read the second 'x', push it onto the stack, and then read 'c'. Based on the value of 'c', the DPDA can transition to an accepting state.
d) None of the mentioned
This option is correct. As explained above, options a) and b) cannot be accepted by a DPDA. Option c) can be accepted by a DPDA, so the correct answer is d) None of the mentioned.
To summarize, a DPDA can accept the language {xxc| where c stands for the complement,{0,1}} but cannot accept the languages of even or odd length palindromes over {a,b}.
A Deterministic Pushdown Automaton (DPDA) is a finite-state machine with a stack that can read input symbols, push or pop symbols from the stack, and transition between states based on the current input symbol and stack symbol.
In order for a string to be accepted by a DPDA, it must follow certain rules and satisfy specific conditions. Let's analyze each of the given options to determine whether they can be accepted by a DPDA.
a) The set of even length palindrome over {a,b}
A palindrome is a string that reads the same forwards and backwards. In this case, we are considering palindromes of even length over the alphabet {a,b}. Since a DPDA has a finite stack, it cannot keep track of an arbitrary number of symbols to ensure that the string is a palindrome. Therefore, a DPDA cannot accept this language.
b) The set of odd length palindrome over {a,b}
Similarly, this language consists of odd length palindromes over the alphabet {a,b}. Again, a DPDA cannot keep track of an arbitrary number of symbols to ensure that the string is a palindrome. Hence, a DPDA cannot accept this language either.
c) {xxc| where c stands for the complement,{0,1}}
This language consists of strings of the form "xxc" where c is the complement of x. The complement of x can be either '0' or '1'. This language can be accepted by a DPDA. The DPDA can read the first 'x', push it onto the stack, read the second 'x', push it onto the stack, and then read 'c'. Based on the value of 'c', the DPDA can transition to an accepting state.
d) None of the mentioned
This option is correct. As explained above, options a) and b) cannot be accepted by a DPDA. Option c) can be accepted by a DPDA, so the correct answer is d) None of the mentioned.
To summarize, a DPDA can accept the language {xxc| where c stands for the complement,{0,1}} but cannot accept the languages of even or odd length palindromes over {a,b}.
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Which of the following can be accepted by a DPDA?a)The set of even length palindrome over {a,b}b)The set of odd length palindrome over {a,b}c){xxc| where c stands for the complement,{0,1}}d)None of the mentionedCorrect answer is option 'D'. Can you explain this answer?
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