# AnswersH5 - University of Central Florida School of Computer Science COT 4210 Spring 2004 Prof Rene Peralta Homework 5:answers to selected problems

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University of Central Florida School of Computer Science COT 4210 Spring 2004 Prof. Rene Peralta Homework 5:answers to selected problems 1. Construct an extended PDA for the language given by the following grammar S aBB + bAA A bAB + a B aBA + b answer: 2. Consider the language L generated by the following grammar. S AT + BR + λ W AT + BR + a + b T WA + a R WB + b A a B b (a) Find a minimum-length string in L which satisﬁes the pumping lemma for CFLs. answer: The idea is to ﬁnd a shortest derivation tree that repeats a variable along a path from the root to a leaf. In the derivation tree below, we see that 1

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S aaTa T aTa We also know T a . Thus the strings aa i aa i are in the language for all i 0. This illustrates the general technique to solve this problem (yielding the candidate answer “aaaa”). In this particular language, however, the strings a i a i are in the language for all i 0 (because of the rule S λ ). So the answer is “aa”.
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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.

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AnswersH5 - University of Central Florida School of Computer Science COT 4210 Spring 2004 Prof Rene Peralta Homework 5:answers to selected problems

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