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On TruthTable Reducibility to SAT
, 2002
"... We show that polynomial time truthtable reducibility via Boolean circuits to SAT is the same as logspace truthtable reducibility via Boolean formulas to SAT and the same as logspace Turing reducibility to SAT . In addition, we prove that a constant number of rounds of parallel queries to SAT i ..."
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Cited by 51 (2 self)
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We show that polynomial time truthtable reducibility via Boolean circuits to SAT is the same as logspace truthtable reducibility via Boolean formulas to SAT and the same as logspace Turing reducibility to SAT . In addition, we prove that a constant number of rounds of parallel queries to SAT is equivalent to one round of parallel queries.
The Role of Relativization in Complexity Theory
 Bulletin of the European Association for Theoretical Computer Science
, 1994
"... Several recent nonrelativizing results in the area of interactive proofs have caused many people to review the importance of relativization. In this paper we take a look at how complexity theorists use and misuse oracle results. We pay special attention to the new interactive proof systems and progr ..."
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Cited by 40 (9 self)
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Several recent nonrelativizing results in the area of interactive proofs have caused many people to review the importance of relativization. In this paper we take a look at how complexity theorists use and misuse oracle results. We pay special attention to the new interactive proof systems and program checking results and try to understand why they do not relativize. We give some new results that may help us to understand these questions better.
The Structure of Complete Degrees
, 1990
"... This paper surveys investigations into how strong these commonalities are. More concretely, we are concerned with: What do NPcomplete sets look like? To what extent are the properties of particular NPcomplete sets, e.g., SAT, shared by all NPcomplete sets? If there are are structural differences ..."
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Cited by 29 (3 self)
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This paper surveys investigations into how strong these commonalities are. More concretely, we are concerned with: What do NPcomplete sets look like? To what extent are the properties of particular NPcomplete sets, e.g., SAT, shared by all NPcomplete sets? If there are are structural differences between NPcomplete sets, what are they and what explains the differences? We make these questions, and the analogous questions for other complexity classes, more precise below. We need first to formalize NPcompleteness. There are a number of competing definitions of NPcompleteness. (See [Har78a, p. 7] for a discussion.) The most common, and the one we use, is based on the notion of mreduction, also known as polynomialtime manyone reduction and Karp reduction. A set A is mreducible to B if and only if there is a (total) polynomialtime computable function f such that for all x, x 2 A () f(x) 2 B: (1) 1
The Isomorphism Conjecture Holds Relative to an Oracle
, 1996
"... We introduce symmetric perfect generic sets. These sets vary from the usual generic sets by allowing limited infinite encoding into the oracle. We then show that the BermanHartmanis isomorphism conjecture [BH77] holds relative to any spgeneric oracle, i.e., for any symmetric perfect generic set A, ..."
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Cited by 26 (11 self)
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We introduce symmetric perfect generic sets. These sets vary from the usual generic sets by allowing limited infinite encoding into the oracle. We then show that the BermanHartmanis isomorphism conjecture [BH77] holds relative to any spgeneric oracle, i.e., for any symmetric perfect generic set A, all NP^Acomplete sets are polynomialtime isomorphic relative to A. Prior to this work there were no known oracles relative to which the isomorphism conjecture held. As part of our proof that the isomorphism conjecture holds relative to symmetric perfect generic sets we also show that P A = FewP A for any symmetric perfect generic A.
On TruthTable Reducibility to SAT and the Difference Hierarchy over NP
, 1987
"... We show that polynomial time truthtable reducibility via Boolean circuits to SAT is the same as log space truthtable reducibility via Boolean formulas to SAT and the same as log space Turing reducibility to SAT . In addition, we prove that a constant number of rounds of parallel queries to SAT ..."
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Cited by 13 (2 self)
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We show that polynomial time truthtable reducibility via Boolean circuits to SAT is the same as log space truthtable reducibility via Boolean formulas to SAT and the same as log space Turing reducibility to SAT . In addition, we prove that a constant number of rounds of parallel queries to SAT is equivalent to one round of parallel queries.
Nonmonotonic reasoning with quantified Boolean constraints
 In Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR97), number 1265 in LNCS
, 1997
"... Abstract. In this paper, we define and investigate the complexity of several nonmonotonic logics with quantified Boolean formulas as constraints. We give quantified constraint versions of the constraint programming formalism of Marek, Nerode, and Remmel [15] and of the natural extension of their the ..."
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Cited by 5 (1 self)
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Abstract. In this paper, we define and investigate the complexity of several nonmonotonic logics with quantified Boolean formulas as constraints. We give quantified constraint versions of the constraint programming formalism of Marek, Nerode, and Remmel [15] and of the natural extension of their theory to default logic. We also introduce a new formalism which adds constraints to circumscription. We show that standard complexity results for each of these formalisms generalize in the quantified constraint case. Gogic, Kautz, Papadimitriou, and Selman [8] have introduced a new method for measuring the strengths of reasoning formalisms based on succinctness of model representation. We show a natural hierarchy based on this measure exists between our versions of logic programming, circumscription, and default logic. Finally, we discuss some results about the relative succinctness of our reasoning formalisms versus any formalism for which model checking can be done somewhere in the polynomial time hierarchy. 1
The size of SPP
 Theoretical Computer Science
"... Derandomization techniques are used to show that at least one of the following holds regarding the size of the counting complexity class SPP. 1. µp(SPP) = 0. 2. PH ⊆ SPP. In other words, SPP is small by being a negligible subset of exponential time or large by containing the entire polynomialtime ..."
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Cited by 4 (1 self)
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Derandomization techniques are used to show that at least one of the following holds regarding the size of the counting complexity class SPP. 1. µp(SPP) = 0. 2. PH ⊆ SPP. In other words, SPP is small by being a negligible subset of exponential time or large by containing the entire polynomialtime hierarchy. This addresses an open problem about the complexity of the graph isomorphism problem: it is not weakly complete for exponential time unless PH is contained in SPP. It is also shown that the polynomialtime hierarchy is contained in SPP NP if NP does not have pmeasure 0. 1