Model-Checking Timed ATL for Durational Concurrent Game Structures

Abstract

Abstract. We extend the framework of ATL model-checking to "simply timed" concurrent game structures, i.e., multi-agent structures where each transition carry an integral duration (or interval thereof). While the case of single durations is easily handled from the semantics point of view, intervals of durations raise several interesting questions. Moreover subtle algorithmic problems have to be handled when dealing with model checking. We propose a semantics for which we develop efficient (PTIME) algorithms for timed ATL without equality constraints, while the general case is shown to be EXPTIME-complete.

Measuring Permissivity in Finite Games

“…This can be seen as the game version of the shortest path problem in weighted automata. Regarding accumulated costs, this was already a by-product of [LMO06]; we show here that for discounted and mean costs, optimal or memoryless optimal strategies do not necessarily exist, but almost-optimal strategies can be obtained as a "pair" of memoryless strategies.…”

“…[LMO06]). Hence, applying Lemma 2 we know that we can solve the optimal reachability problem with penalty in NP: memoryless multi-strategies are sufficient to win optimally, and we can thus guess a memoryless multi-strategy and check, in polynomial time, that it is winning and has penalty less than the given threshold.…”

“…We first prove that our games with penalties can be transformed into classical weighted games [ZP96,LMO06] with an exponential blowup, and that the converse reduction is polynomial.…”

“…The proof is in three steps: first, using our transformation to weighted games and results of [LMO06], we obtain the existence of optimal memoryless multi-strategies; we then propose a polynomialtime algorithm for computing an optimal winning multi-strategy with memory; finally, we show how we can get rid of the memory in such a multi-strategy, which yields the expected result.…”

“…The same kind of mixed objectives is considered when extending ATL with quantitative constraints [LMO06,HP06].…”