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Course: CS 450, Fall 2009
School: Cal Poly Pomona
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Word Count: 191

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Exam CS Final 450 Fall 1989 Craig A. Rich Name: In problems 16, prove the given theorem. 1 Theorem. L1 m L2 L2 m L3 = L1 m L3 . 2 Theorem. L is RE-complete = L m Lu . 3 Theorem. The following decision problem is not recursive: input: question: A DTM M . Is L(M ) regular? 4 Theorem. L1 is RE-complete L1 m L2 = L2 is RE-hard. 5 Theorem. RE L RE = L is RE-complete. Hint: Consider the role of Lu in the...

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Exam CS Final 450 Fall 1989 Craig A. Rich Name: In problems 16, prove the given theorem. 1 Theorem. L1 m L2 L2 m L3 = L1 m L3 . 2 Theorem. L is RE-complete = L m Lu . 3 Theorem. The following decision problem is not recursive: input: question: A DTM M . Is L(M ) regular? 4 Theorem. L1 is RE-complete L1 m L2 = L2 is RE-hard. 5 Theorem. RE L RE = L is RE-complete. Hint: Consider the role of Lu in the proof of Rices theorem, then use the theorem in problem 4. 6 Theorem. The following decision problem is RE-complete: input: question: Hint: the Use theorem in problem 5. A DTM M . Is L(M )? 7 In each of the following, answer true (T) or false (F): a) m is transitive, reexive, and symmetric. b) m is transitive, reexive, and symmetric. c) REC is closed under m . d) EVENS, PRIMES, Lu , Ld , and PCP are R.E. languages. e) Rices theorem implies that it is impossib...

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