On complexity of Ehrenfeucht–Fraïssé games

In this paper, we initiate the study of Ehrenfeucht–Fraïssé games for some standard finite structures. Examples of such standard structures are equivalence relations, trees, unary relation structures, Boolean algebras, and some of their natural expansions. The paper concerns the following question that we call the Ehrenfeucht–Fraïssé problem. Given n∈ω as a parameter, and two relational structures 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 algorithms for solving the Ehrenfeucht–Fraïssé 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.