Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > S -> aSa|bSb|a|b; The language generated ...
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S -> aSa|bSb|a|b; The language generated by the above grammar over the alphabet {a,b} is the set of
- a)All palindromes
- b)All odd length palindromes.
- c)Strings that begin and end with the same symbol
- d)All even length palindromes
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
S -> aSa|bSb|a|b; The language generated by the above grammar over...
The possible palindrome generated by above grammar can be of odd length only as there is no rule for S -> [Tex]epsilon[/Tex] For example generated palindromes are aba, aaa, bab, ababa, aaaaa, ..
Most Upvoted Answer
S -> aSa|bSb|a|b; The language generated by the above grammar over...
Explanation:
The given grammar generates a language over the alphabet {a, b} with the following productions:
S → aSa | bSb | a | b
Let's analyze the productions and determine the properties of the language generated by this grammar.
1. Production S → aSa:
This production allows the generation of palindromes of odd length. It starts and ends with the same symbol 'a' and has a palindrome in the middle. For example, aa, aaa, aaaaa, etc.
2. Production S → bSb:
This production allows the generation of palindromes of odd length. It starts and ends with the same symbol 'b' and has a palindrome in the middle. For example, bb, bbb, bbbbb, etc.
3. Production S → a:
This production allows the generation of strings consisting of a single 'a' symbol. These strings have odd length and can be considered as palindromes.
4. Production S → b:
This production allows the generation of strings consisting of a single 'b' symbol. These strings have odd length and can be considered as palindromes.
Conclusion:
Combining all the productions of the given grammar, we can see that the language generated consists of all possible combinations of palindromes of odd length, regardless of the symbols 'a' and 'b' used. Therefore, the correct answer is option 'B' - All odd length palindromes.
The given grammar generates a language over the alphabet {a, b} with the following productions:
S → aSa | bSb | a | b
Let's analyze the productions and determine the properties of the language generated by this grammar.
1. Production S → aSa:
This production allows the generation of palindromes of odd length. It starts and ends with the same symbol 'a' and has a palindrome in the middle. For example, aa, aaa, aaaaa, etc.
2. Production S → bSb:
This production allows the generation of palindromes of odd length. It starts and ends with the same symbol 'b' and has a palindrome in the middle. For example, bb, bbb, bbbbb, etc.
3. Production S → a:
This production allows the generation of strings consisting of a single 'a' symbol. These strings have odd length and can be considered as palindromes.
4. Production S → b:
This production allows the generation of strings consisting of a single 'b' symbol. These strings have odd length and can be considered as palindromes.
Conclusion:
Combining all the productions of the given grammar, we can see that the language generated consists of all possible combinations of palindromes of odd length, regardless of the symbols 'a' and 'b' used. Therefore, the correct answer is option 'B' - All odd length palindromes.
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S -> aSa|bSb|a|b; The language generated by the above grammar over the alphabet {a,b} is the set ofa)All palindromesb)All odd length palindromes.c)Strings that begin and end with the same symbold)All even length palindromesCorrect answer is option 'B'. Can you explain this answer?
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