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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
TLDR
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
TLDR
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
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