Polynominal time reducibility
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Several of the results that appear in [4] are stated to be true of polynominal time reducibility (≤p) but are not proved explicitly. We shall prove several of these results with the hope of shedding some light on the “determinism vs. nondeterminism” problem. The ideas behind these proofs already exist in [4] but appear here in a different setting. We shall spend most of our time on two theorems: (i) If &fgr; <<subscrpt>p Β then there exists an &Agr; such that &fgr; <<subscrpt>p &Agr; <<subscrpt>p Β and (ii) there exist &Agr; and Β neither of which is polynominal time computable but such that if C ≤p &Agr; and C ≤p Β then C is polynominal time computable. We show how the techniques used in the proofs of these theorems may be extended to prove other results.
[1] Emil L. Post,et al. The Upper Semi-Lattice of Degrees of Recursive Unsolvability , 1954 .
[2] N. A. Lynch. RELATIVIZATION OF THE THEORY OF COMPUTATION COMPLEXITY , 1972 .
[3] Stephen A. Cook,et al. The complexity of theorem-proving procedures , 1971, STOC.