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Q3practicesol

# Q3practicesol - CSE303 Q3 PRACTICE SOLUTIONS YES/NO...

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CSE303 Q3 PRACTICE SOLUTIONS YES/NO questions Circle the correct answer. Write SHORT justification. 1. For any finite language L there is a deterministic automata M , such that L = L ( M ). Justify : Any finite language is regular y 2. Any regular language is finite. Justify : L = a * is infinite n 3. Any finite language is regular. Justify : L = S { L w : w L } , each L w is regular and regular lan- guages are closed under finite union. y 4. Given L 1 , L 2 regular languages over Σ, then ( L 1 * - L 1 )) L 2 is regular. Justify : closure of regular languages over union and complement y 5. For any M , L ( M ) = S { R (1 , j, n ) : q j F } , where R (1 , j, n ) is the set of all strings in Σ * that may drive M from state initial state to state q j without passing through any intermediate state numbered n + 1 or greater, where n is the number of states of M . Justify : only when M is a finite automaton n 6. The Generalized Finite Automaton accepts regular expressions. Justify : accepts regular expressions y 7. There is an algorithm that for any finite automata M computes a regular expression r , such that L ( M ) = r . Justify : defined in the proof of Main Theorem y 8. Pumping Lemma says that we can always prove that a language is regular. Justify : it gives certain characterization of infinite regular languages n 9. Pumping Lemma proves that a language is not regular. Justify : PL is usually used to prove that an infinite language is not regular n 10. L = { a n : n 0 } is not regular. Justify : L = a * n 11. L = { b n a n : n 0 } is not regular. Justify :proved using Pumping Lemma y 12. L = { a 2 n : n 0 } is regular. Justify : L = ( aa ) * y 1

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13. Let L be a regular language, and L 1 L , then L 1 is regular.
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