Positional Strategies in Long Ehrenfeucht-FraïSSé Games

Ehrenfeucht-Fraïssé Games on Random Structures

Certain results in circuit complexity (e.g., the theorem that AC functions have low average sensitivity [5, 17]) imply the existence of winning strategies in Ehrenfeucht-Fräıssé games on pairs of random structures (e.g., ordered random graphs G = G(n, 1/2) and G = G ∪ {random edge}). Standard probabilistic methods in circuit complexity (e.g., the Switching Lemma [11] or Razborov-Smolensky Metho...

Trees and Ehrenfeucht-Fraïssé Games

On Complexity of Ehrenfeucht-Fraïssé Games

In this paper we initiate the study of Ehrenfeucht-Fraı̈ssé 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 Ehrenfeucht-Fraı̈ssé problem. Given n ∈ ω as a parameter, two relational structuresA an...

Almost free groups and Ehrenfeucht-Fraïssé games for successors of singular cardinals

We strengthen non-structure theorems for almost free Abelian groups by studying long Ehrenfeucht-Fräıssé games between a fixed group of cardinality λ and a free Abelian group. A group is called 2-game-free if the isomorphism player has a winning strategy in the game (of the described form) of length 2 ∈ λ. We prove for a large set of successor cardinals λ = μ the existence of nonfree (μ · ω1)-g...

On Winning Strategies in Ehrenfeucht-Fraïssé Games

We present a powerful and versatile new suucient condition for the second player (the \duplicator") to have a winning strategy in an Ehrenfeucht-Fra ss e game on graphs. We accomplish two things with this technique. First, we give a simpler and much easier-to-understand proof of Ajtai and Fagin's result that reachability in directed nite graphs is not in monadic NP. (Monadic NP, otherwise known...