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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 In polynomial time, one can nd accepting paths of nondeterministic polynomial-time Turing machines that accept. Every total multivalued(More)
It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum basis state appears with nonzero amplitude in a superposition, or whether a given quantum bit has positive expectation(More)
We introduce symmetric perfect generic sets. These sets vary from the usual generic sets by allowing limited innnite encoding into the oracle. We then show that the Berman-Hartmanis isomorphism conjecture BH77] holds relative to any sp-generic oracle, i.e., for any symmetric perfect generic set A, all NP A-complete sets are polynomial-time isomorphic(More)
We define and study a new notion called k-immunity that lies between immunity and hyperimmunity in strength. Our interest in k-immunity is justified by the result that ∅ ′ does not k-tt reduce to a k-immune set, which improves a previous result by Kobzev [7, 13]. We apply the result to show that ∅ ′ does not btt-reduce to MIN, the set of minimal programs.(More)
We show how to use various notions of genericity as a tool in oracle creation. We give an abstract deenition of genericity that encompasses a large collection of diierent generic notions. We then show several speciic results: 1. We show how to use standard (Cohen) genericity to create an oracle where the isomorphism conjecture fails in a strong way. 2. We(More)
This paper focuses on complexity classes of partial functions that are computed in polynomial time with oracles in NPMV, the class of all multivalued partial functions that are computable nondeterministically in polynomial time. Concerning deterministic polynomial-time reducibilities, it is shown that 1. A multivalued partial function is polynomial-time(More)
We show that if a language is recognized within certain error bounds by constant-depth quantum circuits over a finite family of gates, then it is computable in (classical) polynomial time. In particular, for 0 < ≤ δ ≤ 1, we define BQNC 0 ,δ to be the class of languages recognized by constant depth, polynomial-size quantum circuits with acceptance(More)