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Unformatted text preview: COT 6315/CIS 4930 (Fall05,Sitharam) Sample test 4 and very brief solutions : for detailed solutions, espe cially proofs, visit TA’s office hours. 1. Classify the following languages as being: (i) neither r.e nor cor.e, (ii) r.e or cor.e (indicate which), but not both; (iii) both r.e. and cor.e but not in PSPACE (iv) In PSPACE, but NPhard (v) in NP but not in Logspace (assuming NP negationslash = Logspace – do not assume NP negationslash = P ) (vi) in P In all cases, fully justify your answer (the reductions, hierarchy theorems, relating space and time complexity classes etc. would be useful). (a) { ( M,z ), M an (always halting) algorithm taking 3 inputs, z ∈ N : ∃ x ∈ N ∀ y ∈ N Maccepts ( x,y,z ) } Answer: (i) – both HALT and complement of HALT are reducible to this set using ≤ rec mreductions. So what? (b) (choose one) { F CNF Boolean formula : strictly greater than 1/2 of all possible truth assignments to the variables of F in fact satisfy F } Answer: (iv) – This is a classical example of a set in the class PP (mentioned briefly in class). Why? It is NPhard since SAT is ≤ P m reducible to it. How?reducible to it....
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This note was uploaded on 01/15/2012 for the course COT 6315 taught by Professor Staff during the Spring '08 term at University of Florida.
 Spring '08
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