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- Stephen A. Fenner, Lance Fortnow, Stuart A. Kurtz
- Structure in Complexity Theory Conference
- 1991

- Stephen A. Fenner, Lance J. Fortnowy, Stuart A. Kurtz
- 1991

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)

- Stephen A. Fenner, Frederic Green, Steven Homer, Randall Pruim
- Electronic Colloquium on Computational Complexity
- 1999

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)

- Stephen A. Fenner, Lance Fortnow, Stuart A. Kurtz, Lide Li
- Inf. Comput.
- 2003

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)

- Stephen A. Fenner, Lance Fortnow, Ashish V. Naik, John D. Rogers
- IEEE Conference on Computational Complexity
- 1996

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)

- Stephen A. Fenner
- Theory of Computing Systems
- 2002

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)

- Stephen A. Fenner
- Structure in Complexity Theory Conference
- 1991

- Stephen A. Fenner, Marcus Schaefer
- Math. Log. Q.
- 1999

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)

- Stephen A. Fenner, Rohit Gurjar, Thomas Thierauf
- Electronic Colloquium on Computational Complexity
- 2015

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 <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)

We study the complexity of inverting many-one, honest, polynomial-time computable onto functions. Asserting that every polynomial-time computable, honest, onto function is invertible is equivalent to the following proposition that we call Q: For all NP machines M that accept , there exists a polynomial-time computable function gM such that for all x, gM(x)… (More)