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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)

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)

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 show that for a wide range of probability measures, constructive gales are interchangable with constructive supergales for defining constructive Hausdorff dimension, thus generalizing a previous independent result of Hitchcock [2] and partially answering an open question of Lutz [5].

2 Abstract The function class #P lacks an important closure property: it is not closed under subtraction. To remedy this problem, we introduce the function class GapP as a natural alternative to #P. GapP is the closure of #P under subtraction, and has all the other useful closure properties of #P as well. We show that most previously studied counting… (More)

We show how to use various notions of genericity as tools in oracle creation. In particular, 1. we give an abstract definition of genericity that encompasses a large collection of different generic notions; 2. we consider a new complexity class AWPP, which contains BQP (quantum polynomial time), and infer several strong collapses relative to SP-generics; 3.… (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)