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Unformatted text preview: gument should • use the fact that R is regular; • use the fact that the intersection between a regular language and a CFL is a CFL; • deﬁne a string z ∈ T for which the pumping lemma for CFL’s does not hold; • a concise and convincing explanation of why z cannot be “pumped”. answer: Assume L is context-free. Since R is regular, T = L ∩ R is context-free. A string z of the form z = ba n bba n bba n b is in T . For n large enough, the pumping lemma for CFL’s must hold for z . Since words in T have exactly six b ’s, z can only be “pumped” at two regions containing only a ’s. The resulting strings are of the form ba k bba l bba m b with k, l, m not necessarily equal. In the latter case, the word cannot be in T , contradiction. Therefore L cannot be context-free. 3...
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This note was uploaded on 06/09/2011 for the course COT 4210 taught by Professor Staff during the Spring '08 term at University of Central Florida.
- Spring '08
- Computer Science