Approximate verification of strategic abilities under imperfect information

Abstract

Model checking of strategic ability under imperfect information is known to be hard. The complexity results range from NP-completeness to undecidability, depending on the precise setup of the problem. No less importantly, fixpoint equivalences do not generally hold for imperfect information strategies, which seriously hampers incremental synthesis of winning strategies.In this paper, we propose translations of ATLir formulae that provide lower and upper bounds for their truth values, and are cheaper to verify than the original specifications. That is, if the expression is verified as true then the corresponding formula of ATLir should also hold in the given model. We begin by showing where the straightforward approach does not work. Then, we propose how it can be modified to obtain guaranteed lower bounds. To this end, we alter the next-step operator in such a way that traversing one's indistinguishability relation is seen as atomic activity. Most interestingly, the lower approximation is provided by a fixpoint expression that uses a nonstandard variant of the next-step ability operator. We show the correctness of the translations, establish their computational complexity, and validate the approach by experiments with a scalable scenario of Bridge play.

Towards Partial Order Reductions for Strategic Ability

“…Asynchronous Simple Voting (ASV). Finally, we propose a new benchmark, inspired by the simple model of voting and coercion from Jamroga et al (2017). There are n voters v 1 , .…”

“…Some early attempts at verification of imperfect information strategies made their way into the MCMAS model checker Raimondi, 2006;Lomuscio et al, 2009Lomuscio et al, , 2017, but the issue has never been at the heart of the tool. Indeed, the recent attempts at practical model checking of imperfect information strategies (Pilecki et al, 2014;Busard et al, 2014;Huang & van der Meyden, 2014;Busard et al, 2015;Jamroga et al, 2019;Kurpiewski et al, 2019aKurpiewski et al, , 2019b confirm that the problem is hard, and dealing with it requires innovative algorithms and verification techniques.…”

Natural strategic ability

“…The former is focused on the way in which ATL and its extensions can be used for verification of multi-agent systems -in particular, what is the complexity of model checking, and how one can overcome the inherent difficulties. An interested reader is referred to [35] for an overview, and to [12,113,118,76,84,39,54,17,77,16,87] for more specific results. Analogous research have been conducted for the more expressive language of Strategy Logic [45,93,90,71].…”

Strategic Abilities of Asynchronous Agents: Semantic Side Effects and How to Tame Them

“…Such statements allow to express important functionality and safety requirements in a simple and intuitive way. Moreover, the provide input to algorithms and tools for verification, that have been in constant development for over 20 years Chen et al 2013;Busard et al 2014;Huang and van der Meyden 2014;Cermák et al 2014;Lomuscio, Qu, and Raimondi 2017;Cermák, Lomuscio, and Murano 2015;Belardinelli et al 2017b;Belardinelli et al 2017a;Jamroga et al 2019;Kurpiewski et al 2021). Asynchronous semantics and partial-order reduction.…”