Results 1  10
of
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 ..."
Abstract
 Add to MetaCart
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 ..."
Abstract

Cited by 416 (37 self)
 Add to MetaCart
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 ..."
Abstract
 Add to MetaCart
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 ..."
Abstract

Cited by 32 (5 self)
 Add to MetaCart
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
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 ..."
Abstract

Cited by 18 (1 self)
 Add to MetaCart
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.
Defeasible Inclusions in LowComplexity DLs: Preliminary Notes
"... We analyze the complexity of reasoning with circumscribed lowcomplexity DLs such as DLlite and the EL family, under suitable restrictions on the use of abnormality predicates. We prove that in circumscribed DLliteR complexity drops from NExpNP to the second level of the polynomial hierarchy. In E ..."
Abstract

Cited by 8 (2 self)
 Add to MetaCart
We analyze the complexity of reasoning with circumscribed lowcomplexity DLs such as DLlite and the EL family, under suitable restrictions on the use of abnormality predicates. We prove that in circumscribed DLliteR complexity drops from NExpNP to the second level of the polynomial hierarchy
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 ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
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
A Novel Relationship Between Dynamics and Complexity in Multiagent Collision Avoidance
"... AbstractThis paper examines the relationship between system dynamics and problem complexity of collision avoidance in multiagent systems. Motivated particularly by results in the field of automated driving, a variant of the reciprocal nbody collision avoidance problem is considered. In this prob ..."
Abstract
 Add to MetaCart
, and that this requirement can change the complexity class of the problem dramatically: from P to NEXP or even NEXP NP . In addition, a constructive proof is provided that demonstrates the relationship and potential realworld applications of the result are discussed.
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 ..."
Abstract

Cited by 22 (6 self)
 Add to MetaCart
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
What can be efficiently reduced to the Kolmogorovrandom strings?
 ANNALS OF PURE AND APPLIED LOGIC
, 2004
"... We investigate the question of whether one can characterize complexity classes (such as PSPACE or NEXP) in terms of efficient reducibility to the set of Kolmogorovrandom strings RC. This question arises because PSPACE ⊆ P RC and NEXP ⊆ NP RC, and no larger complexity classes are known to be reducib ..."
Abstract

Cited by 21 (6 self)
 Add to MetaCart
We investigate the question of whether one can characterize complexity classes (such as PSPACE or NEXP) in terms of efficient reducibility to the set of Kolmogorovrandom strings RC. This question arises because PSPACE ⊆ P RC and NEXP ⊆ NP RC, and no larger complexity classes are known
Results 1  10
of
64