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64
Beyond P^NP = NEXP
"... Buhrman and Torenvliet created an oracle relative to which P NP = NEXP and thus P NP = P NEXP . Their proof uses a delicate finite injury argument that leads to a nonrecursive oracle. We simplify their proof removing the injury to create a recursive oracle making P NP = NEXP. In addition, i ..."
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Buhrman and Torenvliet created an oracle relative to which P NP = NEXP and thus P NP = P NEXP . Their proof uses a delicate finite injury argument that leads to a nonrecursive oracle. We simplify their proof removing the injury to create a recursive oracle making P NP = NEXP. In addition
NonDeterministic Exponential Time has TwoProver Interactive Protocols
"... We determine the exact power of twoprover interactive proof systems introduced by BenOr, Goldwasser, Kilian, and Wigderson (1988). In this system, two allpowerful noncommunicating provers convince a randomizing polynomial time verifier in polynomial time that the input z belongs to the language ..."
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Cited by 416 (37 self)
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are strictly stronger than without, since NEXP # NP. In particular, for the first time, provably polynomial time intractable languages turn out to admit “efficient proof systems’’ since NEXP # P. We show that to prove membership in languages in EXP, the honest provers need the power of EXP only. A consequence
Is BitVector Reasoning as Hard as NExpTime in Practice?
"... It has been shown that (quantifierfree) bitvector logic (BV) is NExpTimecomplete, on account of the fact that the number of propositional variables in the SAT encoding of a BV formula grows exponentially with the length of the declarations of the bitvector variables in the input formula. This le ..."
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It has been shown that (quantifierfree) bitvector logic (BV) is NExpTimecomplete, on account of the fact that the number of propositional variables in the SAT encoding of a BV formula grows exponentially with the length of the declarations of the bitvector variables in the input formula
Recognizing string graphs in NP
 J. of Computer and System Sciences
"... A string graph is the intersection graph of a set of curves in the plane. Each curve is represented by a vertex, and an edge between two vertices means that the corresponding curves intersect. We show that string graphs can be recognized in NP. The recognition problem was not known to be decidable u ..."
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Cited by 32 (5 self)
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A string graph is the intersection graph of a set of curves in the plane. Each curve is represented by a vertex, and an edge between two vertices means that the corresponding curves intersect. We show that string graphs can be recognized in NP. The recognition problem was not known to be decidable
SPLITTING NPCOMPLETE SETS
, 2006
"... We show that a set is mautoreducible if and only if it is mmitotic. This solves a long standing open question in a surprising way. As a consequence of this unconditional result and recent work by Glaßer et al., complete sets for all of the following complexity classes are mmitotic: NP, coNP, â ..."
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Cited by 2 (2 self)
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P, PSPACE, and NEXP, as well as all levels of PH, MODPH, and the Boolean hierarchy over NP. In the cases of NP, PSPACE, NEXP, and PH, this at once answers several wellstudied open questions. These results tell us that complete sets share a redundancy that was not known before. In particular, every NP
The Complexity of Circumscription in Description Logic
"... As fragments of firstorder logic, Description logics (DLs) do not provide nonmonotonic features such as defeasible inheritance and default rules. Since many applications would benefit from the availability of such features, several families of nonmonotonic DLs have been developed that are mostly ba ..."
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Cited by 18 (1 self)
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for NExp NP. It becomes complete for NP NExp when the number of minimized and fixed predicates is bounded by a constant. If roles can be minimized or fixed, then complexity ranges from NExp NP to undecidability. 1.
NP Might Not Be As Easy As Detecting Unique Solutions
, 1997
"... We construct an oracle A such that P A = \PhiP A and NP A = EXP A : This relativized world has several amazing properties: ffl The oracle A gives the first relativized world where one can solve satisfiability on formulae with at most one assignment yet P 6= NP. ffl The oracle A is the fi ..."
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Cited by 22 (6 self)
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We construct an oracle A such that P A = \PhiP A and NP A = EXP A : This relativized world has several amazing properties: ffl The oracle A gives the first relativized world where one can solve satisfiability on formulae with at most one assignment yet P 6= NP. ffl The oracle A
Two Oracles that Force a Big Crunch
, 1999
"... The central theme of this paper is the construction of an oracle A such that NEXP A = P NP A . The construction of this oracle answers a long standing open question rst posed by Heller, and unsuccessfully attacked many times since. For the rst construction of the oracle, we present a new ty ..."
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Cited by 4 (1 self)
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The central theme of this paper is the construction of an oracle A such that NEXP A = P NP A . The construction of this oracle answers a long standing open question rst posed by Heller, and unsuccessfully attacked many times since. For the rst construction of the oracle, we present a new
unknown title
"... We show that circumscription can be used to extend description logics (DLs) with nonmonotonic features in a straightforward and transparent way. In particular, we consider extensions with circumscription of the expressive DLs ALCIO and ALCQO and prove that reasoning in these logics is decidable und ..."
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under a simple restriction: only concept names can be circumscribed, and role names vary freely during circumscription. We pinpoint the exact computational complexity of reasoning as complete for NP NEXP and NEXP NP, depending on whether or not the number of minimized and fixed predicates is assumed
unknown title
"... We show that circumscription can be used to extend description logics (DLs) with nonmonotonic features in a straightforward and transparent way. In particular, we consider extensions with circumscription of the expressive DLs ALCIO and ALCQO and prove that reasoning in these logics is decidable und ..."
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under a simple restriction: only concept names can be circumscribed, and role names vary freely during circumscription. We pinpoint the exact computational complexity of reasoning as complete for NP NEXP and NEXP NP, depending on whether or not the number of minimized and fixed predicates is assumed
Results 1  10
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64