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Consider the three problems :
- Equivalence
- Ambiguity
- Regularity
- a)Regular and context free grammars are closed in all three problems
- b)Regular grammar is closed in equivalence and regularity but not in Ambiguity
- c)Regular grammar is closed in all three but CFL is not closed in anyone
- d)Regular and CFL grammar is closed in equivalence and regularity but not in Ambiguity
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Consider the three problems : Equivalence Ambiguity Regularitya)Regula...
For regular language
1) Equivalence: it can be checked by developed product automate for XOR function.
if XOR = O ⇒ equal else not.
2) Ambiguity: Ambiguity is decidable for regular languages & grammar since they are deterministic in nature.
3) Regularity: it is the trivial problem.
For context free language
⇒ it is not closed in any of those problems.
Most Upvoted Answer
Consider the three problems : Equivalence Ambiguity Regularitya)Regula...
Explanation:
The given statement is about the closure properties of regular and context-free grammars with respect to three problems: equivalence, ambiguity, and regularity. Let's understand each problem and its closure properties in detail.
1. Equivalence:
- Two grammars are said to be equivalent if they generate the same language.
- Closure property:
- Regular grammars are closed under equivalence, which means if two regular grammars generate the same language, then their union, concatenation, and Kleene closure also generate the same language.
- Context-free grammars (CFL) are not closed under equivalence. There is no algorithm to determine whether two CFLs generate the same language or not.
2. Ambiguity:
- A grammar is said to be ambiguous if there exist multiple parse trees for a single string.
- Closure property:
- Regular grammars are not closed under ambiguity. Regular grammars always generate unambiguous languages.
- Context-free grammars are not closed under ambiguity as well. There is no algorithm to determine whether a CFL is ambiguous or not.
3. Regularity:
- A language is regular if it can be generated by a regular grammar or recognized by a finite automaton.
- Closure property:
- Regular grammars are closed under regularity. The union, concatenation, and Kleene closure of regular grammars also generate regular languages.
- Context-free grammars are not closed under regularity. The union and concatenation of CFLs may not generate a CFL. However, the Kleene closure of a CFL always generates a CFL.
Conclusion:
From the given options, option 'C' is correct because regular grammars are closed in all three problems (equivalence, ambiguity, and regularity), whereas CFLs are not closed in any of these problems.
The given statement is about the closure properties of regular and context-free grammars with respect to three problems: equivalence, ambiguity, and regularity. Let's understand each problem and its closure properties in detail.
1. Equivalence:
- Two grammars are said to be equivalent if they generate the same language.
- Closure property:
- Regular grammars are closed under equivalence, which means if two regular grammars generate the same language, then their union, concatenation, and Kleene closure also generate the same language.
- Context-free grammars (CFL) are not closed under equivalence. There is no algorithm to determine whether two CFLs generate the same language or not.
2. Ambiguity:
- A grammar is said to be ambiguous if there exist multiple parse trees for a single string.
- Closure property:
- Regular grammars are not closed under ambiguity. Regular grammars always generate unambiguous languages.
- Context-free grammars are not closed under ambiguity as well. There is no algorithm to determine whether a CFL is ambiguous or not.
3. Regularity:
- A language is regular if it can be generated by a regular grammar or recognized by a finite automaton.
- Closure property:
- Regular grammars are closed under regularity. The union, concatenation, and Kleene closure of regular grammars also generate regular languages.
- Context-free grammars are not closed under regularity. The union and concatenation of CFLs may not generate a CFL. However, the Kleene closure of a CFL always generates a CFL.
Conclusion:
From the given options, option 'C' is correct because regular grammars are closed in all three problems (equivalence, ambiguity, and regularity), whereas CFLs are not closed in any of these problems.
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Consider the three problems : Equivalence Ambiguity Regularitya)Regular and context free grammars are closed in all three problemsb)Regular grammar is closed in equivalence and regularity but not in Ambiguityc)Regular grammar is closed in all three but CFL is not closed in anyoned)Regular and CFL grammar is closed in equivalence and regularity but not in AmbiguityCorrect answer is option 'C'. Can you explain this answer?
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Consider the three problems : Equivalence Ambiguity Regularitya)Regular and context free grammars are closed in all three problemsb)Regular grammar is closed in equivalence and regularity but not in Ambiguityc)Regular grammar is closed in all three but CFL is not closed in anyoned)Regular and CFL grammar is closed in equivalence and regularity but not in AmbiguityCorrect answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider the three problems : Equivalence Ambiguity Regularitya)Regular and context free grammars are closed in all three problemsb)Regular grammar is closed in equivalence and regularity but not in Ambiguityc)Regular grammar is closed in all three but CFL is not closed in anyoned)Regular and CFL grammar is closed in equivalence and regularity but not in AmbiguityCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the three problems : Equivalence Ambiguity Regularitya)Regular and context free grammars are closed in all three problemsb)Regular grammar is closed in equivalence and regularity but not in Ambiguityc)Regular grammar is closed in all three but CFL is not closed in anyoned)Regular and CFL grammar is closed in equivalence and regularity but not in AmbiguityCorrect answer is option 'C'. Can you explain this answer?.
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