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

are strictly stronger than without, since NEXP # NP. In particular, for the first time, prov-ably 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

It has been shown that (quantifier-free) bit-vector logic (BV) is NExpTime-complete, 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 bit-vector variables in the input formula

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

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.

We analyze the complexity of reasoning with circumscribed low-complexity DLs such as DL-lite and the EL family, under suitable restrictions on the use of abnormality predicates. We prove that in circumscribed DL-liteR complexity drops from NExpNP to the second level of the polynomial hierarchy

Š•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 well-studied open questions. These results tell us that complete sets share a redundancy that was not known before. In particular, every NP

, 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.

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

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 Kolmogorov-random strings RC. This question arises because PSPACE ⊆ P RC and NEXP ⊆ NP RC, and no larger complexity classes are known