Journal ArticleDOI
The Boolean hierarchy II: applications
Jin-Yi Cai,Thomas Gundermann,Gerd Wechsung,Juris Hartmanis,Lane A. Hemachandra,Vivian Sewelson,Klaus W. Wagner +6 more
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The Boolean Hierarchy I: Structural Properties explores the structure of the boolean hierarchy, the closure of NP with respect to boolean hierarchies, and the role of symbols in this hierarchy.Abstract:
The Boolean Hierarchy I: Structural Properties [J. Cai et al., SIAM J. Comput ., 17 (1988), pp. 1232–252] explores the structure of the boolean hierarchy, the closure of NP with respect to boolean ...read more
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Book ChapterDOI
A catalog of complexity classes
TL;DR: This chapter discusses the concepts needed for defining the complexity classes, a set of problems of related resource-based complexity that can be solved by an abstract machine M using O(f(n) of resource R, where n is the size of the input.
Book
Introduction to the theory of complexity
TL;DR: 1. Mathematical Preliminaries, Elements of Computability Theory, and Space-Complexity Classes: Algorithms and Complexity Classes.
Journal ArticleDOI
The strong exponential hierarchy collapses
TL;DR: It is shown that the strong exponential hierarchy collapses to P NE, its Δ 2 level, using the use of partial census information and the exploitation of nondeterminism.
Journal ArticleDOI
On truth-table reducibility to SAT
Samuel R. Buss,Louise Hay +1 more
TL;DR: It is shown that polynomial time truth-table reducibility via Boolean circuits to SAT is the same as logspace truth- table reducibilities via Boolean formulas to SAT and the sameAs logspace Turing reducible to SAT.
Journal ArticleDOI
The complexity of matrix rank and feasible systems of linear equations
TL;DR: It is shown that this natural complexity class for which the problems of determining if a system of linear equations is feasible and computing the rank of an integer matrix are complete under logspace reductions is closed under NC1-reducibility.