We study the complexity of nding the values and optimal strategies of mean payoo games on graphs, a family of perfect information games introduced by Ehrenfeucht and Mycielski and considered by Gurvich, Karzanov and Khachiyan. We describe a pseudo-polynomial time algorithm for the solution of such games, the decision problem for which is in NP \ co-NP. Finally, we describe a polynomial reductio...

∗BASED ON A TALK PRESENTED AT “NEW INSIGHTS IN QUANTUM MECHANICS – FUNDAMENTALS, EXPERIMENTAL RESULTS, THEORETICAL DIRECTIONS”, GOSLAR, AUGUST 31 – SEPTEMBER 3, 1998. Let us mention just some of them: T.W.B. Kibble , A. Ashtekar and T.A. Schilling , P. Bona , R. Haag and U. Bannier , Mielnik , S. Weinberg , G. Auberson and P.C. Sabatier , M.D. Kostin , H.D. Doebner and Goldin , I. Bialynicki-Bi...

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...

We prove that if a graph embeds on a surface with all edges suitably short, then the vertices of the graph can be five-colored. The motivation is that a graph embedded with short edges is locally a planar graph and hence should not require many more than four colors. Introduction. It is well known [4, 15] that a graph embedded on a surface of genus k > 0, the sphere with k handles, can always b...

We prove the existence of a free group of rotations of rank 2 which acts on the rational unit sphere without non-trivial fixed points. Introduction. The purpose of this paper is to prove that the group SO3(Q) of all proper orthogonal 3 × 3 matrices with rational entries has a free subgroup F2 of rank 2 such that for all w ∈ F2 different from the identity and for all ~r ∈ S2 ∩Q3 we have w(~r ) 6...

(compacta) and continuous mappings was founded by Shchepin [Sh]. He described some elementary properties of such functors and defined the notion of the normal functor which has become very fruitful. The classes of all normal and weakly normal functors include many classical constructions: the hyperspace exp, the space of probability measures P, the superextension λ , the space of hyperspaces of...

This paper is a continuation of [8]. Let A and B be two first order structures of the same vocabulary L. We denote the domains of A and B by A and B respectively. All vocabularies are assumed to be relational. The Ehrenfeucht-Fräıssé-game of length γ of A and B denoted by EFGγ(A,B) is defined as follows: There are two players called ∀ and ∃. First ∀ plays x0 and then ∃ plays y0. After this ∀ pl...

Assuming some basic familiarity with ordinal arithmetic, we provide a friendly introduction to the theory of Ehrenfeucht-Fräıssé games. 1 What Is An Ehrenfeucht-Fräıssé Game? Ehrenfeucht-Fräıssé (EF) games were first developed in the 50’s and 60’s by Andrzej Ehrenfeucht and Roland Fräıssé. Although Fräıssé developed much of the background theory and some important applications in his doctoral d...