Inverting onto functions

Abstract

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: In polynomial time, one can find accepting paths of nondeterministic polynomial-time Turing machines that accept Σ*. Every total multivalued nondeterministic function has a polynomial-time computable refinement. In polynomial time, one can compute satisfying assignments for any polynomial-time computable set of satisfiable formulae. In polynomial time, one can convert the accepting computations of any nondeterministic Turing machine that accepts SAT to satisfying assignments.