Playing with Repetitions in Data Words Using Energy Games

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