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Ehrenfeucht-Fraisse games provide means to characterize elementary equivalence for first-order logic, and by standard translation also for modal logics. We propose a novel generalization of Ehrenfeucht- Fraisse games to hybrid-dynamic…

Logic in Computer Science · Computer Science 2025-06-12 Guillermo Badia , Daniel Gaina , Alexander Knapp , Tomasz Kowalski , Martin Wirsing

Truth, consistency and elementary equivalence can all be characterised in terms of games, namely the so-called evaluation game, the model-existence game, and the Ehrenfeucht-Fraisse game. We point out the great affinity of these games to…

Logic · Mathematics 2023-03-23 Jouko Väänänen

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…

Logic in Computer Science · Computer Science 2021-07-27 Samson Abramsky , Nihil Shah

Let (A) and (B) be two first order structures of the same vocabulary. We shall consider the Ehrenfeucht-Fra{i}sse-game of length omega_1 of A and B which we denote by G_{omega_1}(A,B). This game is like the ordinary Ehrenfeucht-Fraisse-game…

Logic · Mathematics 2009-09-25 Alan H. Mekler , Saharon Shelah , Jouko Väänänen

A number of model-comparison games central to (finite) model theory, such as pebble and Ehrenfeucht-Fra\"{i}ss\'{e} games, can be captured as comonads on categories of relational structures. In particular, the coalgebras for these comonads…

Logic in Computer Science · Computer Science 2025-05-07 Samson Abramsky , Thomas Laure , Luca Reggio

We consider two-player games played over finite state spaces for an infinite number of rounds. At each state, the players simultaneously choose moves; the moves determine a successor state. It is often advantageous for players to choose…

Logic in Computer Science · Computer Science 2015-07-01 Luca de Alfaro , Rupak Majumdar , Vishwanath Raman , Mariëlle Stoelinga

Two structures A and B are n-equivalent if player II has a winning strategy in the n-move Ehrenfeucht-Fraisse game on A and B. We extend earlier results about n-equivalence for finite coloured linear orders, describing an algorithm for…

Logic · Mathematics 2017-05-15 Feresiano Mwesigye , John K Truss

Game comonads offer a categorical view of a number of model-comparison games central to model theory, such as pebble and Ehrenfeucht-Fra\"iss\'e games. Remarkably, the categories of coalgebras for these comonads capture preservation of…

Logic in Computer Science · Computer Science 2024-07-02 Samson Abramsky , Luca Reggio

We study the class of word-building games, where two players pick letters from a finite alphabet to construct a finite or infinite word. The outcome is determined by whether the resulting word lies in a prescribed set (a win for player $A$)…

Dynamical Systems · Mathematics 2015-01-19 Ville Salo , Ilkka Törmä

In classical Maker-Breaker games on graphs, Maker and Breaker take turns claiming edges; Maker's goal is to claim all of some structure (e.g., a spanning tree, Hamilton cycle, etc.), while Breaker aims to stop her. The standard question…

Combinatorics · Mathematics 2025-05-28 Wesley Pegden , Francesca Yu

In this paper we will discuss scoring play games. We will give the basic definitions for scoring play games, and show that they form a well defined set, with clear and distinct outcome classes under these definitions. We will also show that…

Combinatorics · Mathematics 2012-11-08 Fraser Stewart

Positional games are a mathematical class of two-player games comprising Tic-tac-toe and its generalizations. We propose a novel encoding of these games into Quantified Boolean Formulas (QBFs) such that a game instance admits a winning…

Logic in Computer Science · Computer Science 2023-11-03 Valentin Mayer-Eichberger , Abdallah Saffidine

Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…

Logic in Computer Science · Computer Science 2009-08-28 Samuel Mimram

Ehrenfeucht-Fra\"iss\'e games provide a fundamental method for proving elementary equivalence (and equivalence up to a certain quantifier rank) of relational structures. We investigate the soundness and completeness of this method in the…

Logic in Computer Science · Computer Science 2023-08-10 Sophie Brinke , Erich Grädel , Lovro Mrkonjić

First-order (FO) transition systems have recently attracted attention for the verification of parametric systems such as network protocols, software-defined networks or multi-agent workflows like conference management systems. Desirable…

Logic in Computer Science · Computer Science 2019-11-15 Helmut Seidl , Christian Müller , Bernd Finkbeiner

We study two-player games with alternating moves played on infinite trees. Our main focus is on the case where the trees are full (regular) and the winning set is open (with respect to the product topology on the tree). Gale and Stewart…

Optimization and Control · Mathematics 2026-02-17 Dean Kraizberg

In this paper, we explore the descriptive complexity theory of finite groups by examining the power of the second Ehrenfeucht-Fraisse bijective pebble game in Hella's (Ann. Pure Appl. Log., 1989) hierarchy. This is a Spoiler-Duplicator game…

Logic in Computer Science · Computer Science 2023-10-03 Joshua A. Grochow , Michael Levet

In this paper, we give an overview of some recent work on applying tools from category theory in finite model theory, descriptive complexity, constraint satisfaction, and combinatorics. The motivations for this work come from Computer…

Logic in Computer Science · Computer Science 2023-06-22 Samson Abramsky

Game semantics describe the interactive behavior of proofs by interpreting formulas as games on which proofs induce strategies. Such a semantics is introduced here for capturing dependencies induced by quantifications in first-order…

Logic in Computer Science · Computer Science 2011-01-27 Samuel Mimram

In this paper, we explore the descriptive complexity theory of finite groups by examining the power of the second Ehrenfeucht--Fra\"iss\'e bijective pebble game in Hella's (Ann. Pure Appl. Log., 1989) hierarchy. This is a…

Logic in Computer Science · Computer Science 2025-11-12 Joshua A. Grochow , Michael Levet