Computer Science 500

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Computer Science 500 Spring, 1999 Tuesday, May
6 Final Thurday May 13 10am-12
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L1 M L(M) not equal to null set L2 M
L(M) is infinite L3 M L(M) is infinite and
L(M) is infinite L4 M L(M) is equal to
Lu L5 M L(M) equals 11,00
For each Li, a) write Li in Kleene form b) Is
Li recognizable? (prove) c) Is Li
co-recognizable? (prove)
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Final topics

• I DFA/NFA/Regular Expressions
• Pumping Lemma (and contrapositive)
• NFA to DFA conversion
• Regular Expression to NFA conversion
• DFA to Regular Expression conversion
• Practice writing NFAs

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• II Decidability Theory
• Turing Machine Design
• Decidable/Recognizable/co-recognizable
• Diagonalization
• Kleene notation
• Reductions/Completeness
• Rices Theorem and applications

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• III Complexity Theory
• time complexity, P, NP, co-NP, polynomial
• time hierarchy
• poly-time reductions
• Cook/Levin Theorem, SAT, 3-SAT
• NP-completeness proofs
• PSPACE, TQBF is PSPACE complete
• time hierachy theorem
• RP, co-RP, BPP, IP