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Assume the statements S1 and S2 given as:
S1: Given a context free grammar, there exists an algorithm for determining whether L (G) is infinite.
S2: There exists an algorithm to determine whether two context free grammars generate the same language.
Which of the following is true?
  • a)
    S1 is correct and S2 is not correct
  • b)
    Both S1 and S2 are correct
  • c)
    Both S1 and S2 are not correct
  • d)
    S1 is not correct and S2 is correct
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Assume the statements S1 and S2 given as:S1: Given a context free gram...
 The proof of S1 can be seen in various book of theory of computation but s2 is a problem of category undecidable so a contradiction to this assumption can be easily obtained.
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Most Upvoted Answer
Assume the statements S1 and S2 given as:S1: Given a context free gram...
Explanation:

To determine whether the given statements S1 and S2 are correct or not, let's evaluate each statement individually.

S1: Given a context-free grammar, there exists an algorithm for determining whether L(G) is infinite.

This statement is correct. There exists an algorithm called the pumping lemma for context-free languages that can be used to determine whether a language generated by a context-free grammar is infinite or not. The pumping lemma states that if there exists a string in the language that is larger than the number of non-terminals in the grammar, then it can be divided into five parts (uvwxy) such that for any i >= 0, the string u(v^i)w(x^i)y is also in the language. Using this lemma, we can construct an algorithm to determine whether L(G) is infinite.

S2: There exists an algorithm to determine whether two context-free grammars generate the same language.

This statement is not correct. It is undecidable whether two context-free grammars generate the same language. This is known as the equivalence problem for context-free grammars and it has been proven to be undecidable. Therefore, there does not exist an algorithm that can determine whether two context-free grammars generate the same language.

Conclusion:

Based on the evaluation of the two statements, we can conclude that S1 is correct and S2 is not correct. Therefore, the correct answer is option 'A'.
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Assume the statements S1 and S2 given as:S1: Given a context free grammar, there exists an algorithm for determining whether L (G) is infinite.S2: There exists an algorithm to determine whether two context free grammars generate the same language.Which of the following is true?a)S1 is correct and S2 is not correctb)Both S1 and S2 are correctc)Both S1 and S2 are not correctd)S1 is not correct and S2 is correctCorrect answer is option 'A'. Can you explain this answer?
Question Description
Assume the statements S1 and S2 given as:S1: Given a context free grammar, there exists an algorithm for determining whether L (G) is infinite.S2: There exists an algorithm to determine whether two context free grammars generate the same language.Which of the following is true?a)S1 is correct and S2 is not correctb)Both S1 and S2 are correctc)Both S1 and S2 are not correctd)S1 is not correct and S2 is correctCorrect answer is option 'A'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Assume the statements S1 and S2 given as:S1: Given a context free grammar, there exists an algorithm for determining whether L (G) is infinite.S2: There exists an algorithm to determine whether two context free grammars generate the same language.Which of the following is true?a)S1 is correct and S2 is not correctb)Both S1 and S2 are correctc)Both S1 and S2 are not correctd)S1 is not correct and S2 is correctCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Assume the statements S1 and S2 given as:S1: Given a context free grammar, there exists an algorithm for determining whether L (G) is infinite.S2: There exists an algorithm to determine whether two context free grammars generate the same language.Which of the following is true?a)S1 is correct and S2 is not correctb)Both S1 and S2 are correctc)Both S1 and S2 are not correctd)S1 is not correct and S2 is correctCorrect answer is option 'A'. Can you explain this answer?.
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