Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Which of the following assertion is false?a)I...
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Which of the following assertion is false?
- a)If L is a language accepted by PDA1 by final state, there exist a PDA2 that accepts L by empty stack i.e. L=L(PDA1)=L(PDA2)
- b)If L is a CFL then there exists a push down automata P accepting CF; ; by empty stack i.e. L=M(P)
- c)Let L is a language accepted by PDA1 then there exist a CFG X such that L(X)=M(P)
- d)All of the mentioned
Correct answer is option 'D'. Can you explain this answer?
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Which of the following assertion is false?a)If L is a language accepte...
All the assertions mentioned are theorems or corollary.
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Which of the following assertion is false?a)If L is a language accepte...
Explanation:
The false assertion in the given options is option D, which states that "All of the mentioned" are false. Let's analyze each option to understand why.
a) If L is a language accepted by PDA1 by final state, there exists a PDA2 that accepts L by empty stack i.e. L=L(PDA1)=L(PDA2)
This statement is true. If a language L is accepted by a pushdown automaton (PDA) PDA1 by final state, then we can construct another PDA PDA2 such that it accepts the same language L by empty stack. The idea is to replace the final states of PDA1 with empty stack transitions in PDA2. Therefore, option a) is true.
b) If L is a CFL, then there exists a pushdown automaton P accepting L by empty stack i.e. L=M(P)
This statement is also true. It is a well-known result in formal language theory that every context-free language (CFL) can be recognized by a pushdown automaton with an empty stack. So, for every CFL L, there exists a PDA P that accepts L by empty stack. Therefore, option b) is true.
c) Let L be a language accepted by PDA1, then there exists a CFG X such that L(X)=M(P)
This statement is true as well. Given a language L accepted by a PDA PDA1, we can construct a context-free grammar (CFG) X such that L(X) = L(PDA1). This is known as the "PDA to CFG conversion" process, where the nonterminals of the CFG correspond to the states of the PDA and the production rules are derived based on the transitions of the PDA. Therefore, option c) is true.
d) All of the mentioned
Since options a), b), and c) are all true, the assertion "All of the mentioned" cannot be false. Therefore, option d) is false.
Conclusion:
The false assertion among the given options is option d) "All of the mentioned". Options a), b), and c) are all true and supported by well-known results in formal language theory.
The false assertion in the given options is option D, which states that "All of the mentioned" are false. Let's analyze each option to understand why.
a) If L is a language accepted by PDA1 by final state, there exists a PDA2 that accepts L by empty stack i.e. L=L(PDA1)=L(PDA2)
This statement is true. If a language L is accepted by a pushdown automaton (PDA) PDA1 by final state, then we can construct another PDA PDA2 such that it accepts the same language L by empty stack. The idea is to replace the final states of PDA1 with empty stack transitions in PDA2. Therefore, option a) is true.
b) If L is a CFL, then there exists a pushdown automaton P accepting L by empty stack i.e. L=M(P)
This statement is also true. It is a well-known result in formal language theory that every context-free language (CFL) can be recognized by a pushdown automaton with an empty stack. So, for every CFL L, there exists a PDA P that accepts L by empty stack. Therefore, option b) is true.
c) Let L be a language accepted by PDA1, then there exists a CFG X such that L(X)=M(P)
This statement is true as well. Given a language L accepted by a PDA PDA1, we can construct a context-free grammar (CFG) X such that L(X) = L(PDA1). This is known as the "PDA to CFG conversion" process, where the nonterminals of the CFG correspond to the states of the PDA and the production rules are derived based on the transitions of the PDA. Therefore, option c) is true.
d) All of the mentioned
Since options a), b), and c) are all true, the assertion "All of the mentioned" cannot be false. Therefore, option d) is false.
Conclusion:
The false assertion among the given options is option d) "All of the mentioned". Options a), b), and c) are all true and supported by well-known results in formal language theory.
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Which of the following assertion is false?a)If L is a language accepted by PDA1 by final state, there exist a PDA2 that accepts L by empty stack i.e. L=L(PDA1)=L(PDA2)b)If L is a CFL then there exists a push down automata P accepting CF; ; by empty stack i.e. L=M(P)c)Let L is a language accepted by PDA1 then there exist a CFG X such that L(X)=M(P)d)All of the mentionedCorrect answer is option 'D'. Can you explain this answer?
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