Stephen A. Fenner

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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 classes,(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 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 polynomialtime Turing machines that accept Σ∗. • Every total multivalued(More)
Abstract. We show that the counting classes AWPP and APP [FFKL], [L] are more robust than previously thought. Our results identify a sufficient condition for a language to be low for PP, and we show that this condition is at least as weak as other previously studied criteria. We extend a result of Köbler et al. by proving that all sparse co-C = P languages(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. Other(More)
We show that the bipartite perfect matching problem is in quasi- <i>NC</i><sup>2</sup>. That is, it has uniform circuits of quasi-polynomial size&#xA0;<i>n</i><sup><i>O</i>(log<i>n</i>)</sup>, and <i>O</i>(log<sup>2</sup> <i>n</i>) depth. Previously, only an exponential upper bound was known on the size of such circuits with poly-logarithmic depth. We(More)