We generalize the concept of a break by considering pairs of arbitrary rounds. We show that a set of home-away patterns minimizing the number of generalized breaks cannot be found in polynomial time, unless P=NP. When all teams have the same break set, the decision version becomes easy; optimizing remains NP-hard.

We study the shrinking and separation properties (two notions well-known in descriptive set theory) for NP and coNP and show that under reasonable complexity-theoretic assumptions, both properties do not hold for NP and the shrinking property does not hold for coNP. In particular we obtain the following results. 1. NP and coNP do not have the shrinking property, unless PH is finite. In general,...

Buhrman and Torenvliet created an oracle relative to which P NP = NEXP and thus P NP = P NEXP. Their proof uses a delicate nite 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, in our construction we can make P = UP = NP \ coNP. This leads to the curious situation where LOW(NP) = P but ...

Human ttributions of intelligence in others reflect heuristic judgments of superficial qualities rather than systematic analysis of competence. This article reviews the literature on attribution of intelligence in humans and machines, examines the public controversy over human intelligence, mid extrapolates to the subject of machine intelligence. The possible effects on public policy ale discus...

The problem of computing the range y of a given function f(x1, . . . , xn) over given intervals xi – often called the main problem of interval computations – is, in general, NP-hard. This means that unless P = NP, it is not possible to have a feasible (= polynomial time) algorithm that always computes the desired range. Instead, interval computations algorithms compute an enclosure Y ⊇ y for th...

This paper is an attempt to provide a JLO-type formula for a bivariant Chern character defined on “families of spectral triples”. Such families should be viewed as an algebraic version of unbounded Kasparov bimodules. The Chern character is built from the exponential of the curvature of a superconnection, leading to a heat kernel regularization of traces. We work within the Cuntz-Quillen formal...

In order to cooperate effectively with its peers, an agent must manipulate representations of the social structures in which it plays a part. The purpose of this paper is to investigate the mathematical and computational aspects of this social reasoning process. We begin by defining an abstract representation of cooperation structures, wherein agents cooperate to achieve goals on each other’s b...

This is the third article in a series of four articles dealing with the P vs. NP question. The purpose of this work is to demonstrate that although the oracle relativizations of the NP complexity class eliminate some methods as possible routes to a solution, the methods used in the first two articles of this series are not affected by oracle relativizations. Furthermore, the solution to the P v...

This is a survey of work on proof complexity and proof search from a logicoalgorithmic viewpoint, as motivated by the P versus NP problem. We discuss propositional proof complexity, Cook’s program, proof automatizability, proof search, algorithms for satisfiability, and the state of the art of our (in)ability to separate P and NP .