Playing with Repetitions in Data Words Using Energy Games

TL;DR

This paper introduces two-player games over infinite data words, analyzing the decidability of winning strategies and establishing a connection between logic of repeating values and energy games.

Contribution

It presents a novel game-theoretic framework for data words and links the logic of repeating values to decidable energy games, extending previous logical and automata results.

Findings

Deciding winning strategies is undecidable in general.

Restricting to Boolean valuations yields decidable energy game equivalents.

Establishes a new connection between data word logics and energy games.

Abstract

We introduce two-player games which build words over infinite alphabets, and we study the problem of checking the existence of winning strategies. These games are played by two players, who take turns in choosing valuations for variables ranging over an infinite data domain, thus generating multi-attributed data words. The winner of the game is specified by formulas in the Logic of Repeating Values, which can reason about repetitions of data values in infinite data words. We prove that it is undecidable to check if one of the players has a winning strategy, even in very restrictive settings. However, we prove that if one of the players is restricted to choose valuations ranging over the Boolean domain, the games are effectively equivalent to single-sided games on vector addition systems with states (in which one of the players can change control states but cannot change counter values), known to be decidable and effectively equivalent to energy games. Previous works have shown that the satisfiability problem for various variants of the logic of repeating values is equivalent to the reachability and coverability problems in vector addition systems. Our results raise this connection to the level of games, augmenting further the associations between logics on data words and counter systems.