Reducing the number of solutions of NP functions
Journal of Computer and System Sciences
Reducing the Number of Solutions of NP Functions
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
Graph Isomorphism Is Low for ZPP(NP) and Other Lowness Results
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
Is the Standard Proof System for SAT P-Optimal?
FST TCS 2000 Proceedings of the 20th Conference on Foundations of Software Technology and Theoretical Computer Science
On a P-optimal Proof System for the Set of All Satisfiable Boolean Formulas (SAT)
MCU '01 Proceedings of the Third International Conference on Machines, Computations, and Universality
One-way permutations and self-witnessing languages
Journal of Computer and System Sciences
The Shrinking Property for NP and coNP
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
The shrinking property for NP and coNP
Theoretical Computer Science
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We look at the hypothesis that all honest onto polynomial-time computable functions have a polynomial-time computable inverse. We show this hypothesis equivalent to several other complexity conjectures including: One can find accepting paths of nondeterministic polynomial-time Turing machines that accept Sigma^*. Every total multivalued nondeterministic function has a polynomial-time computable refinement. One can compute satisfying assignments for any polynomial-time computable set of satisfiable formulae. One can convert the accepting computations of any nondeterministic Turing machine that accepts SAT to satisfying assignments. We compare these hypotheses with several other important complexity statements. We also examine the complexity of these statements where we only require a single bit instead of the entire inverse, path, etc.