Generalized Ehrenfeucht games

Trees and Ehrenfeucht-Fraïssé Games

The Ehrenfeucht-Fraisse Games for Transitive Closure

We present in this paper Ehrenfeucht-Frai"sse games for the transitiveclosure logics DTC, TC and ATC. Although the existence of such games for logics with generalized quantifiers was known before, the exact formulation of these games for the predicate transformers arising from various transitive-closure-like operations is new. The games are sound and complete both for finite and infinite models...

On winning strategies in Ehrenfeucht-Frai’ssk games

We present a powerful and versatile new sufficient condition for the second player (the “duplicator”) to have a winning strategy in an Ehrenfeucht-Fra’isst 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 finite graphs is not in monadic NP. (Monadic NP, otherwise k...

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...

On winning Ehrenfeucht games and monadic NP

Inexpressibility results in Finite Model Theory are often proved by showing that Duplicator, one of the two players of an Ehrenfeucht game, has a winning strategy on certain structures. In this article a new method is introduced that allows, under certain conditions, the extension of a winning strategy of Duplicator on some small parts of two nite structures to a global winning strategy. As app...