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c318f94t3 - Prove that L(P U L(R is a subset of L(P U...

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CSc 318 Exam 3 Friday 2 December 1994 (1) (15 pts) Find a minimal complete DFA equivalent to the DFA ({s,1,2,3,4}, {a,b}, { (s,a,1), (s,b,2), (1,a,3), (1,b,2), (3,a,3), (3,b,s), (2,a,4), (2,b,2), (4,a,3), (4,b,s)}, s, {3,4} ) (2) (15 pts) Find an NFA with the same language as the lambda-NFA ({s,2,3,4}, {a,b}, {(s,a,2), (s,lambda,2), (2,b,3), (2,lambda,3), (s,b,4), (4,a,4), (4,lambda,3)}, s, {3} ) (3) (20 pts) Prove that for every complete DFA there is an EFA with the same language. (4) (20 pts) Let P and R be lambda-NFAs with disjoint state symbols.
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Unformatted text preview: Prove that L(P) U L(R) is a subset of L(P U R). (5) (10 pts) Prove that (making believe the *'s and .'s are superscripts) [ [ [ [a U b]* U a] . [a . b]] U c]* is a regular expression over the alphabet {a,b,c,d}. (6) (10 pts) Find a CFG which is not left-recursive and equivalent to the CFG S --> Sab | Sbc | aSb | c (7) (10 pts) Given the CFG, G, given below, find a lambda-free CFG, G', such that L(G')=L(G)-{lambda}. S --> abSbScSd | lambda...
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