The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Complexity of finitely presented algebras
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Comparison of polynomial-time reducibilities
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
Indexing of subrecursive classes
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
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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; p &Bgr; then there exists an &Agr; such that &fgr; p &Agr; p &Bgr; and (ii) there exist &Agr; and &Bgr; neither of which is polynominal time computable but such that if C ≤p &Agr; and C ≤p &Bgr; 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.