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2000-Automata_and_Formal_Languages-scanned

2000-Automata_and_Formal_Languages-scanned - Comprehensive...

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Comprehensive Exam: Autumn 2000-01 Automat a and Formal Languages (60 points) Problem 1. [lo points] Consider the language L defined by the regular expression 00'10. Provide a PDA M for this language using as few states as possible. Note that there is a PDA with only 1 state and that the number of points you get will depend on the number of states used in your solution. Problem 2. [18 points] Decide whether the following statements are TRUE or FALSE. You will receive 3 points for each correct answer and -2 points for each incorrect answer. 1. If L1 and L2 are both non-regular, then L1 n L2 must be non-regular. 2. L = {w E {a, b, c)' ( w does not contain an equal number of occurrences of a, 6, and c) is context-free. 3. Let L represent the language of a non-deterministic finite-state automaton N; then, swapping the final and non-final states of N gives a machine N' whose language is the complement of L. 4. Assume that P # NP. If L1 is in P and L2 is in NP, then L1 n L2 must be in P.
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  • '08
  • Motwani,R
  • Computational complexity theory, Formal language, Halting problem, NP-complete, Boolean satisfiability problem

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