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MidTerm1SampleQuestionsKey

# MidTerm1SampleQuestionsKey - COT 4210 Fall 2009 Sample...

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COT 4210 Fall 2009 Sample Problems Key 1. Draw a DFA to recognize the set of strings over {a,b}* that contain the same number of occurrences of the substring ab as of the substring ba . 2 . Present the transition diagram or table for a DFA that accepts the regular set denoted by the expression (0+1)* (010 + 11) (0 + 1)* 0 1 > < λ > <0> <1> <0> <0> <01> <01> <010+11> <010+11> <1> <0> <010+11> <010+11> <010+11> <010+11> 3. Consider the following assertion: Let R be a regular language, then any set S , such that S R = S , is also regular. State whether you believe this statement to be True or False by circling your answer. TRUE FALSE If you believe that this assertion is True, present a convincing argument (not formal proof) to back up your conjecture. If you believe that it is False, present a counterexample using known regular and non-regular languages, R and S , respectively. Let R = φ and S = a n b n ; S R = a n b n = S , but S is not regular. 4. Assume that L 1 and L 1 L 2 are both regular languages. Is L 2 necessarily a regular language? If so, prove this, otherwise show that L 2 could either be regular or non-regular. L 2 could either be regular or non-regular L 2 regular: L 1 = φ ; L 2 = φ ; L 1 L 2 = φ L 2 non-regular: L 1 = φ ; L 2 = a n b n ; L 1 L 2 = φ λ a b ba ab a b b b a a b b a

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COT 42110 – 2 – 5. Let L be defined as the language accepted by the finite state automaton A : a.) Fill in the following table, showing the λ -closures for each of A ’s states. State A B C D E λ -closure { A } { B , C } { C } { D, E } { E } b.) Convert A to an equivalent deterministic finite state automaton. Use states like AC to denote the subset of states {A,C} .
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• Spring '10
• Icamarra
• Formal language, Regular expression, Regular language, Nondeterministic finite state machine, finite state automaton

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