Let L be the set of all strings over the alphabet {a, b, c} which satisfy all of

Question

Let L be the set of all strings over the alphabet {a, b, c} which satisfy all of the following properties. If the string does not contain any b, s then the string contains an odd number of c's; if the string contains exactly one be then the string is a palindrome: if the string contains exactly two b's then the string is a concatenation of two palindromes: if the string contains more than two b's the the string contains exactly one a and no c's. Write a complete formal definition of a context-free grammar that generates the language L. If such a grammar does not exist, state it and explain why.

Explanation / Answer

a. a*c(ca*c U a)*

b. c*ac*a(a U b)* U a*ca*ca*

c. a*ba*b(a U b)*

d. L e | a | b | c | aUa | bUb | cUc.

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