Games on Strings with a Limited Order Relation

Authors:
Elisabetta Maria;Angelo Montanari;Nicola Vitacolonna
Affiliations:
Department of Mathematics and Computer Science, University of Udine, Italy;Department of Mathematics and Computer Science, University of Udine, Italy;Department of Mathematics and Computer Science, University of Udine, Italy
Venue:
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
Year:
2009

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Abstract

In this paper, we show how Ehrenfeucht-Fraïssé games can be successfully exploited to compare (finite) strings. More precisely, we give necessary and sufficient conditions for Spoiler/Duplicator to win games played on finite structures with a limited order relation, that lies in between the successor relation and the usual (linear) order relation, and a finite number of unary predicates. On the basis of such conditions, we outline a polynomial (in the size of the input strings) algorithm to compute the "remoteness" of a game and to determine the optimal strategies/moves for both players.