154 research outputs found
Weak Ehrenfeucht-Fraïssé Games
In this paper we define a game which is played between two players I and II on two mathematical structures A and B. The players choose elements from both structures in moves, and at the end of the game the player II wins if the chosen structures are isomorphic. Thus the difference of this to the ordinary Ehrenfeucht-Fra¨ıss´e game is that the isomorphism can be arbitrary, whereas in the ordinary EF-game it is determined by the moves of the players. We investigate determinacy of the weak EF-game for different (the length of the game) and its relation to the ordinary EF-game.Peer reviewe
Ehrenfeucht-Fraïssé games without identity
This note defines Ehrenfeucht-Fraïssé games where identity is not present in the basic language. The formulation is applied to show that there is no elementary theory in the language of one binary relation that exactly characterizes models in which the relation is the identity relation
Ehrenfeucht-Fraïssé games without identity
This note defines Ehrenfeucht-Fraïssé games where identity is not present in the basic language. The formulation is applied to show that there is no elementary theory in the language of one binary relation that exactly characterizes models in which the relation is the identity relation
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 Ehrenfeucht-Fraïssé problem. Given n ϵ ω as a parameter, 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 G_n (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
Inherent Complexity of Recursive Queries
AbstractWe give lower bounds on the complexity of certain Datalog queries. Our notion of complexity applies to compile-time optimization techniques for Datalog; thus, our results indicate limitations of these techniques. The main new tool is linear first-order formulas, whose depth (respectively, number of variables) matches the sequential (respectively, parallel) complexity of Datalog programs. We define a combinatorial game (a variant of Ehrenfeucht–Fraı̈ssé games) that can be used to prove nonexpressibility by linear formulas. We thus obtain lower bounds for the sequential and parallel complexity of Datalog queries. We prove syntactically tight versions of our results, by exploiting uniformity and invariance properties of Datalog queries
Relating Structure and Power: Comonadic Semantics for Computational Resources
Combinatorial games are widely used in finite model theory, constraint
satisfaction, modal logic and concurrency theory to characterize logical
equivalences between structures. In particular, Ehrenfeucht-Fraisse games,
pebble games, and bisimulation games play a central role. We show how each of
these types of games can be described in terms of an indexed family of comonads
on the category of relational structures and homomorphisms. The index k is a
resource parameter which bounds the degree of access to the underlying
structure. The coKleisli categories for these comonads can be used to give
syntax-free characterizations of a wide range of important logical
equivalences. Moreover, the coalgebras for these indexed comonads can be used
to characterize key combinatorial parameters: tree-depth for the
Ehrenfeucht-Fraisse comonad, tree-width for the pebbling comonad, and
synchronization-tree depth for the modal unfolding comonad. These results pave
the way for systematic connections between two major branches of the field of
logic in computer science which hitherto have been almost disjoint: categorical
semantics, and finite and algorithmic model theory.Comment: To appear in Proceedings of Computer Science Logic 201
Ehrenfeucht-Fraïssé goes elementarily automatic for structures of bounded degree
International audienceMany relational structures are automatically presentable, i.e. elements of the domain can be seen as words over a finite alphabet and equality and other atomic relations are represented with finite automata. The first-order theories over such structures are known to be primitive recursive, which is shown by the inductive construction of an automaton representing any relation definable in the first-order logic. We propose a general method based on Ehrenfeucht-Fraïssé games to give upper bounds on the size of these automata and on the time required to build them. We apply this method for two different automatic structures which have elementary decision procedures, Presburger Arithmetic and automatic structures of bounded degree. For the latter no upper bound on the size of the automata was known. We conclude that the very general and simple automata-based algorithm works well to decide the first-order theories over these structures
How to win a game with features
We show, that the axiomatization of rational trees in the language of features given elsewhere is complete. In contrast to other completeness proofs that have been given in this field, we employ the method of Ehrenfeucht-Fraïssé Games, which yields a much simpler proof. The result extends previous results on complete axiomatizations of rational trees in the language of constructor equations or in a weaker feature language
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