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Midterm 2 Solution Fall 2013

At the lower left it should not say ca instead it

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Unformatted text preview: | ε; C → cC | ε; R → aRb | aA | bB; T → bTc | cC | bB.) So this language can be pumped because it is a CFL. The DCFLs are closed under complementation, so consider the complement of L. It is {aibici : i ≥ 0} ∪ Σ*baΣ* ∪ Σ*caΣ*∪ Σ*cbΣ* where Σ = {a,b,c}. The CFLs are not in general closed under intersection, but the intersection of a CFL and a regular language is a CFL (We saw this using the “product construction” that we used to show that regular languages are closed under intersection.) So intersect the complement of L with a*b*c* to get {aibici : i ≥ 0}. Because this is not a CFL (by pumping, as we have seen many times), the complement of L is not a CFL. But then because D...
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