Games for Counting Abstractions

It has been recently shown that monotonicity is not sufficient to obtain decidability results for two-player games. However, positive results can be obtained on restricted subclasses of monotonic two-player games. In this paper, we identify and study a subclass of monotonic two-player games that is useful for analysis of parametric (open) systems that can be modeled by using counting abstractions. Although the reachability game problem is undecidable in general for that subclass, we identify two interesting and decidable problems and show how to apply those results in parametric system analysis.