Under the hypothesis that NP does not have p-measure 0 (roughly, that NP contains more than a negligible subset of exponential time), it is show n that there is a language that is P T -complete (\Cook complete"), but not P m -complete (\Karp-Levin complete"), for NP. This conclusion, widely believed to be true, is not known to follow from P 6= NP or other traditional complexity-theoretic hypoth...

This paper introduces a knowledge recognition algorithm (KRA) that is both a Turing machine algorithm and an Oracle Turing machine algorithm. By definition KRA is a non-deterministic language recognition algorithm. Simultaneously it can be implemented as a deterministic Turing machine algorithm. KRA applies mirrored perceptual-conceptual languages to learn member-class relations between the two...

complexity Reductions, hardness, completeness Projections, provers and verifiers Complexity 3: Feasibility Dusko Pavlovic Introduction Time and space Abstract complexity Reducibility P vs NP Outline Introduction: Gödel’s letter Time and space complexity

In this primarily expository article, I describe geometric approaches to variants of P v. NP , present several results that illustrate the role of group actions in complexity theory, and make a first step towards geometric definitions of complexity classes. My goal is to help bring geometry and complexity theory closer together.

We consider the problem of characterizing the stability of effectivity functions (EFF), via a correspondence between game theoretic and well-known combinatorial concepts. To every EFF we assign a pair of hypergraphs, representing clique covers of two associated graphs, and obtain some necessary and some sufficient conditions for the stability of EFFs in terms of graphproperties. These condition...

Gerechte designs are a specialisation of latin squares. A gerechte design is an n×n array containing the symbols {1, . . . , n}, together with a partition of the cells of the array into n regions of n cells each. The entries in the cells are required to be such that each row, column and region contains each symbol exactly once. We show that the problem of deciding if a gerechte design exists fo...

In this paper we present the model of decision P systems with external output and prove the following main result: if there exists an NP–complete problem that cannot be solved in polynomial time, with regard to the input length, by the deterministic variant of such P systems, constructed in polynomial time, then P 6= NP . From Zandron-FerretiMauri’s theorem it follows that if P 6= NP then no NP...

We address the problem of enumerating all models of Boolean formulæ in order of non-decreasing weight in Schaefer’s framework. The weight of a model is the number of variables assigned to 1. Tractability in this context amounts to enumerating all models one after the other in sorted order, with polynomial delay between two successive outputs. The question of model-enumeration has already been s...

We study envy-free pricing mechanisms in matching markets with m items and n budget constrained buyers. Each buyer is interested in a subset of the items on sale, and she appraises at some single-value every item in her preference-set. Moreover, each buyer has a budget that constraints the maximum affordable payment, while she aims to obtain as many items as possible of her preference-set. Our ...

The crossing number of a graph G is the minimum number of crossings in a drawing of G. The determination of the crossing number is an NP-complete problem. We present two general lower bounds for the crossing number, and survey their applications and generalizations.