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The language L = {WbcWR | W ∈ (a+b)*} is _____.
- a)DCFL
- b)CFL but not DCFL
- c)Non-CFL
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
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The language L = {WbcWR| W ∈ (a+b)*} is _____.a)DCFLb)CFL but not...
Any language for which we can have a Deterministic PDA is always a DCFL. Here for language L= {WbcWR | W ∈ (a+b)*} we can have a PDA with following transitions in which PDA accepts a string when it halts on a final state. q0 in initial state and qf is final state. 1. (q0, a , Z) -> (q0, aZ) 2. (q0, b , Z) -> (q0, bZ) 3. (q0, a , a) ->(q0, aa) 4. (q0, b , a) -> (q0, ba) 5. (q0, a, b) -> (q0, ab) 6. (q0, b , b) -> (q0, bb) 7. (q0, c , b) -> (q1, null) 8. (q1, a , a) ->(q1, null) 9. (q1, b , b) -> (q1, null) 10. (q1, null, Z ) -> (qf, Z) Here all a’s and b’s are initially pushed onto the stack for W. As soon as a c occurs after b , B is popped from the stack after which W^R is checked. If the further string alphabets match the alphabet of the stack the alphabet is popped from the stack and finally the string reaches the final state if language is of the form L= {WbcW^R | W ∈ (a+b)*}. Hence the above language is a DCFL.
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The language L = {WbcWR| W ∈ (a+b)*} is _____.a)DCFLb)CFL but not...
Is the set of all strings that have the form WbcWR, where W is any string, b is a single 'b' character, c is a single 'c' character, and WR is the reverse of W.
For example, the string "abcba" would be in L because W = "a" and WR = "a", so WbcWR = "abcba". Similarly, the string "xyzbcbazyx" would also be in L because W = "xyz" and WR = "zyx", so WbcWR = "xyzbcbazyx".
However, the string "abcbazyx" would not be in L because there is no possible W such that WbcWR would result in "abcbazyx".
In summary, L is the language of all strings that can be formed by taking any string, adding a 'b' and 'c' in between, and then adding the reverse of the original string.
For example, the string "abcba" would be in L because W = "a" and WR = "a", so WbcWR = "abcba". Similarly, the string "xyzbcbazyx" would also be in L because W = "xyz" and WR = "zyx", so WbcWR = "xyzbcbazyx".
However, the string "abcbazyx" would not be in L because there is no possible W such that WbcWR would result in "abcbazyx".
In summary, L is the language of all strings that can be formed by taking any string, adding a 'b' and 'c' in between, and then adding the reverse of the original string.
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The language L = {WbcWR| W ∈ (a+b)*} is _____.a)DCFLb)CFL but not DCFLc)Non-CFLd)None of the aboveCorrect answer is option 'A'. Can you explain this answer?
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