A tournament is a complete graph with its edges directed, and colouring a tournament means partitioning its vertex set into transitive subtournaments. For some tournaments H there exists c such that every tournament not containing H as a subtournament has chromatic number at most c (we call such a tournament H a hero); for instance, all tournaments with at most four vertices are heroes. In this...

We observe that ranking systems—a theoretical framework for web page ranking and collaborative filtering introduced by Altman and Tennenholtz—and tournament solutions—a well-studied area of social choice theory—are strongly related. This relationship permits a mutual transfer of axioms and solution concepts. As a first step, we formally analyze a tournament solution that is based on Google’s Pa...

Tournament selection is one of the most popular selection operators in Genetic Algorithms. Recently, its popularity is increasing because this operator is well suited for Parallel Genetic Algorithms applications. In this paper, new selection operator is proposed. The new operator, which should be an improvement of the tournament selection, is named “Fine-grained Tournament Selection” (FGTS). It...

In this paper, we propose a new notion of rep-cube which is a net of a cube, and it can be divided into some polygons such that each of them can be folded to a cube. This notion is inspired by polyomino and rep-tile; both are introduced by Solomon W. Golomb, and well investigated in the recreational mathematics society. We prove that there are infintely many distinct rep-cubes. We also extend t...

Functional transductions realized by two-way transducers (equivalently, by streaming transducers and by MSO transductions) are the natural and standard notion of"regular"mappings from words to words. It was shown in 2013 that it is decidable if such a transduction can be implemented by some one-way transducer, but the given algorithm has non-elementary complexity. We provide an algorithm of dif...

The task of understanding the dynamics of coevolutionary algorithms or comparing performance between such algorithms is complicated by the fact the internal fitness measures are subjective. Though several techniques have been proposed to use external or objective measures to help in analysis, there are clearly properties of fitness payoff, like intransitivity, for which these techniques are ine...

How Many Winners Are Good to Have? On Tournaments with Sabotage From an employer’s perspective a tournament should induce agents to exert productive activities but refrain from destructive ones. We experimentally test the predictive power of a tournament model which suggests that – within a reasonable framework – productive and destructive activities are not influenced neither by the number of ...

In this paper, we motivate and describe a term long game tournament. The tournament has different milestones, including breadth first search, heuristic search, knowledge representation and reasoning and the tournament proper. For this last milestone, students are encouraged to use machine learning techniques. We describe in detail each of the milestones as well as the game and its specification...

We study the closure of regular languages by taking subwords or superwords, provide exact state complexity in the case of unbounded alphabets, and prove new lower bounds in the case of languages over a two-letter alphabet. We also consider the dual interior sets, for which the nondeterministic state complexity has a doubly-exponential upper bound and for which we prove matching doublyexponentia...