The following technical report is available from http://aib.informatik.rwth-aachen.de:
Parametric LTL Games Martin Zimmermann AIB 2010-11
We consider graph games of infinite duration with winning conditions in parameterized linear temporal logic, where the temporal operators are equipped with variables for time bounds. In model checking such specifications were introduced as PLTL by Alur et al. and (in a different version called PROMPT-LTL) by Kupferman et al..
Our work lifts their results on model checking for PLTL and PROMPT-LTL to the level of games: we present algorithms that determine whether a player wins a game with respect to some, infinitely many, or all variable valuations. All these algorithms run in doubly-exponential time; so, adding bounded temporal operators does not increase the complexity compared to solving plain LTL games. Furthermore, we show how to determine optimal valuations that allow a player to win a game.