• Publications
  • Influence
A complexity theory for feasible closure properties
The study of the complexity of sets encompasses two complementary aims: (1) establishing—usually via explicit construction of algorithms-that sets are feasible, and (2) studying the relativeExpand
The strong exponential hierarchy collapses
The polynomial hierarchy, composed of the levels P, NP, PNP, NPNP, etc., plays a central role in classifying the complexity of feasible computations. It is not known whether the polynomial hierarchyExpand
Collapsing degrees via strong computation
An equivalence class with respect to a given type of reduction is called a degree. It is natural to expect that using more flexible reduction types will increase the size of a degree. When using moreExpand
The strong exponential hierarchy collapses
Abstract Composed of the levels E (i.e., ∪ c DTIME[2 cn ]), NE, P NE , NP NE , etc., the strong exponential hierarchy is an exponential-time analogue of the polynomial-time hierarchy. This paperExpand
On the Power of Probabilistic Polynomial Time:PNP[log] ⊆ PP
We show that every set in the 0~ level of the polynomial hierarchy-every set polynomial­ time truth-table reducible to SAT~is accepted by a probabilistic polynomial-time Turing machine: pNP[log] ~Expand
Promises and fault-tolerant database access
It is given both structural and relativized evidence that fault tolerant access to UP suffices to recognize even sets beyond UP, and completely characterize the complexity classes R and ZPP in terms of fault-tolerant database access. Expand
Counting in structural complexity theory
Structural complexity theory is the study of the form and meaning of computational complexity classes. Complexity classes--P, NP, ProbabilisticP, PSPACE, etc.--are formalizations of computationalExpand
Structure of Complexity Classes: Separations, Collapses, and Completeness
During the last few years, unprecedented progress has been made in structural complexity theory; class inclusions and relativized separations were discovered, and hierarchies collapsed. We surveyExpand
A complexity theory for feasible closure properties
The authors show natural operations-such as subtraction and division-to be hard closure properties, in the sense that if a class is closed under one of these, then it has all feasible closure properties. Expand