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2004-Automata_and_Formal_Languages-scanned

# 2004-Automata_and_Formal_Languages-scanned - Automata and...

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Automata and Formal Languages Comprehensive Exam Fall 2004 Problem 1 (10 points) Give context-free grammars generating the following languages over the alphabet {O,1) (you need not prove the correctness of your grammm): (a) {aida*j+kb'6 : i, j, k > 0); (b) all strings with an equal number of a's and b's. Problem 2 (15 points) Decide whether the following statements are TRUE or FALSE. You will receive 3 points for each correct answer and -2 points for each incowect answer. (a) If LI and L2 are both non-regular, then L1 n L2 must be non-regular. (b) Suppose there is a polynomial-time reduction from the language L1 to the language L2. It is possible that L1 is solvable in polynomial time but Lz is not even in NP. (c) Suppose there is a polynomial-time reduction from the language L1 to the language L2. If L1 is recursive, then La must be recursive. (d) Every infinite regular set contains a subset that is not recursively enumerable. (e) Every infinite recursively enumerable set contains an infinite subset that is recursive.

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2004-Automata_and_Formal_Languages-scanned - Automata and...

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