Let Cbe the language over {a, b,c, d, e, f} accepting all strings so that: 1.There are precisely two b’s in the string. 2.Every a is immediately followed by an odd number of e’s.
Let Cbe the language over {a, b,c, d, e, f} accepting all strings so that:
1.There are precisely two b’s in the string.
2.Every a is immediately followed by an odd number of e’s.
3.Every d is immediately followed by an even number of f’s.
4.e’s and f’s don’t occur except as provided in rules 2 and 3.
5.All a’s occur after the first b.
6.All d’s occur before the second b.
7.In between the two b’s there are exactly twice as many a’s as d’s.HINT:
Don’t be intimidated by the number of rules. The way they interact actually helps you simplify the number of cases you have to deal with while constructing this grammar.
a. Construct a context-free grammar generating C.Explain how your construction accounts for each rule.
b. We could eliminate one rule from Cand make it regular. Which rule would that be, and why would it work? You do not need a formal proof, but you do need an explanation.
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