On a monadic NP vs monadic co-NP
Information and Computation
On winning strategies in Ehrenfeucht-Fraïssé games
Theoretical Computer Science
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
On the Ehrenfeucht-Fraïssé Game in Theoretical Computer Science
TAPSOFT '93 Proceedings of the International Joint Conference CAAP/FASE on Theory and Practice of Software Development
Computational Complexity of Ehrenfeucht-Fraïssé Games on Finite Structures
Proceedings of the 12th International Workshop on Computer Science Logic
Games on Strings with a Limited Order Relation
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
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Ehrenfeucht-Fraïssé games are commonly used as a method to measure the expressive power of a logic, but they are also a flexible tool to compare structures. To exploit such a comparison power, explicit conditions characterizing the winning strategies for both players must be provided. We give a necessary and sufficient condition for Duplicator to win games played on finite structures with a successor relation and a finite number of unary predicates. This structural characterization suggests an algorithmic approach to the analysis of games, which can be used to compute the “remoteness” of a game and to determine the optimal moves for both players, that is, to derive algorithms for Spoiler and Duplicator that play optimally. We argue that such an algorithmic solution may be used in contexts where the “degree of similarity” between two structures must be measured, such as the comparison of biological sequences.