Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
On the Structure of Polynomial Time Reducibility
Journal of the ACM (JACM)
An Introduction to the General Theory of Algorithms
An Introduction to the General Theory of Algorithms
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
A note on one-way functions and polynomial-time isomorphisms
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Minimal degrees for polynomial reducibilities
Journal of the ACM (JACM)
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In this abstract and discussion of forthcoming papers, we will be concerned with variations on a common theme: without assuming a solution to P vs NP, what can one say of a general nature that relates structural properties of general classes of sets in NP to reducibilities among these sets? By “structural” we mean, in ways that will become clearer as we proceed, properties which arise from general definitions rather than properties which may arise from a perhaps more “natural” computational point of view. Although quite a bit is known about such questions relative to oracles or relative to the assumption that P @@@@ NP, in so far as possible we wish to obtain absolute results; that is results which are about sets in NP (not relativized) and which can be obtained without assuming a solution to P vs NP. In a final section summarizing our results we will make some general comments about the historical antecedents and possible future significance of this approach.