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Unformatted text preview: are required if P is re: – If L is in (has property) P and L ’ some re set L’, then L’ is in P. – If L is an infinite set in P, then there is some finite subset L’ of L that is in P. – The set of finite languages in P is enumerable. 10/4/11 Dec 2, © UCF (Charles E. 77 Using Extended Rice • Violate Condition # 1 – L = “ – L is recursive – L is a singleton set – L is a regular set • Violates Condition # 2 – L = “ * • Violates Condition # 3 10/4/11 Dec 2, © UCF (Charles E. 88 RE Sets • L ” “ • L contains at least 3 numbers • W is in L, for a fixed W • L & Lu & ± 10/4/11 Dec 2, © UCF (Charles E. 99 Minimum Quantification • Recursive: unquantified total predicate • RE: existentially quantified • ~ RE: universally quantified • Recursive: Can express as RE & ~RE • TOT: universal/existential • ~TOT: existential/universal...
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 Spring '08
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 Set Theory, Recursion, Quantification, Charles E

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