On Complexity of Ehrenfeucht-Fra¨ õss´ eG ames

In this paper we initiate the study of Ehrenfeucht-Fra¨õsse games for some standard finite structures. Examples of such standard structures are equiv- alence relations, trees, unary relation structures, Boolean algebras, and some of their natural expansions. The paper concerns the following question that we call Ehrenfeucht-Fra¨ õsse problem. Given n ∈ ω as a parameter, two relational struc- tures A and B from one of the classes of structures mentioned above, how efficient is it to decide if Duplicator wins the n-round EF game Gn(A, B)? We provide al- gorithms for solving the Ehrenfeucht-Fra¨ õsse problem for the mentioned classes of structures. The running times of all the algorithms are bounded by constants. We obtain the values of these constants as functions of n.