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cot6410F10FinalSampleQuestions

# cot6410F10FinalSampleQuestions - COT 6410 Fall 2010 Final...

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COT 6410 Fall 2010 Final Exam Sample Questions 1 . Let set A be recursive, B be re non-recursive and C be non-re. Choosing from among (REC) recursive , (RE) re non-recursive , (NR) non-re , categorize the set D in each of a) through d) by listing all possible categories. No justification is required. a.) D = ~C b.) D (A C) c.) D = ~B d.) D = B - A 2. Prove that the Halting Problem (the set K 0 ) is not recursive (decidable) within any formal model of computation. (Hint: A diagonalization proof is required here.) 3. Using reduction from the known undecidable HasZero, HZ = { f | 5 x f(x) = 0 } , show the non- recursiveness (undecidability) of the problem to decide if an arbitrary primitive recursive function g has the property IsZero, Z = { f | 2200 x f(x) = 0 } . 4 . Choosing from among (D) decidable , (U) undecidable , (?) unknown , categorize each of the following decision problems. No proofs are required. Problem / Language Class Regular Context Free Context Sensitive L = Σ * ? L = φ ? L = L 2 ? x L 2 , for arbitrary x ?

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