# hw5 - L 1 ⊕ L 2 is inﬁnite and L 1 ∩ L 2 is...

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University of Central Florida School of Computer Science COT 4210 Spring 2004 Prof. Rene Peralta Homework 5 Due date: March 31 1. Construct an extended PDA for the language given by the following grammar S aBB + bAA A bAB + a B aBA + b 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. (b) Find a non-empty string u L such that u i L for all i 0. (c) Find strings u,v such that | u | ≥ 6, v 6 = λ , and such that u i v L for all i 0. 3. (a) Find L 1 ,L 2 such that the symmetric diﬀerence L 1 L 2 is inﬁnite and L 1 L 2 is not context-free. (b) Find non-regular CFLs L 1 ,L 2 such that the symmetric diﬀerence
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Unformatted text preview: L 1 ⊕ L 2 is inﬁnite and L 1 ∩ L 2 is context-free. 4. Consider the type of automaton that you obtain by replacing the stack in a PDA by a queue. Let us call this type of machine a FIFO-automaton. For simplicity, assume FIFO-automata accept by accepting state only. • Brieﬂy explain how a FIFO automaton can implement “PUSH(X,Q)” (add X to the front of Q ), “TAIL(Q)” (read the tail element in Q ), and “REMOVE-TAIL(Q)” (remove the tail element in Q ). • Does there exist a non-context free language L that is accepted by a FIFO-automaton? Justify your answer. 1...
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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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