Verifying existence of resource-bounded coalition uniform strategies

We consider the problem of whether a coalition of agents has a knowledge-based strategy to ensure some outcome under a resource bound. We extend previous work on verification of multi-agent systems where actions of agents produce and consume resources, by adding epistemic pre- and postconditions to actions. This allows us to model scenarios where agents perform both actions which change the world, and actions which change their knowledge about the world, such as observation and communication. To avoid logical omniscience and obtain a compact model of the system, our model of agents’ knowledge is syntactic.We define a class of coalition-uniform strategies with respect to any (decidable) notion of coalition knowledge. We show that the model-checking problem for the resulting logic is decidable for any notion of coalition uniform strategies in these classes

Strategy Logic with Imperfect Information

We introduce an extension of Strategy Logic for the imperfect-information setting, called SLii, and study its model-checking problem. As this logic naturally captures multi-player games with imperfect information, the problem turns out to be undecidable. We introduce a syntactical class of "hierarchical instances" for which, intuitively, as one goes down the syntactic tree of the formula, strategy quantifications are concerned with finer observations of the model. We prove that model-checking SLii restricted to hierarchical instances is decidable. This result, because it allows for complex patterns of existential and universal quantification on strategies, greatly generalises previous ones, such as decidability of multi-player games with imperfect information and hierarchical observations, and decidability of distributed synthesis for hierarchical systems. To establish the decidability result, we introduce and study QCTL*ii, an extension of QCTL* (itself an extension of CTL* with second-order quantification over atomic propositions) by parameterising its quantifiers with observations. The simple syntax of QCTL* ii allows us to provide a conceptually neat reduction of SLii to QCTL*ii that separates concerns, allowing one to forget about strategies and players and focus solely on second-order quantification. While the model-checking problem of QCTL*ii is, in general, undecidable, we identify a syntactic fragment of hierarchical formulas and prove, using an automata-theoretic approach, that it is decidable. The decidability result for SLii follows since the reduction maps hierarchical instances of SLii to hierarchical formulas of QCTL*ii

ATLsc with partial observation

Alternating-time temporal logic with strategy contexts (ATLsc) is a powerful formalism for expressing properties of multi-agent systems: it extends CTL with strategy quantifiers, offering a convenient way of expressing both collaboration and antagonism between several agents. Incomplete observation of the state space is a desirable feature in such a framework, but it quickly leads to undecidable verification problems. In this paper, we prove that uniform incomplete observation (where all players have the same observation) preserves decidability of the model-checking problem, even for very expressive logics such as ATLsc.Comment: In Proceedings GandALF 2015, arXiv:1509.0685

Reasoning about Knowledge and Strategies under Hierarchical Information

Two distinct semantics have been considered for knowledge in the context of strategic reasoning, depending on whether players know each other's strategy or not. The problem of distributed synthesis for epistemic temporal specifications is known to be undecidable for the latter semantics, already on systems with hierarchical information. However, for the other, uninformed semantics, the problem is decidable on such systems. In this work we generalise this result by introducing an epistemic extension of Strategy Logic with imperfect information. The semantics of knowledge operators is uninformed, and captures agents that can change observation power when they change strategies. We solve the model-checking problem on a class of "hierarchical instances", which provides a solution to a vast class of strategic problems with epistemic temporal specifications on hierarchical systems, such as distributed synthesis or rational synthesis

Model Checking One-clock Priced Timed Automata

We consider the model of priced (a.k.a. weighted) timed automata, an extension of timed automata with cost information on both locations and transitions, and we study various model-checking problems for that model based on extensions of classical temporal logics with cost constraints on modalities. We prove that, under the assumption that the model has only one clock, model-checking this class of models against the logic WCTL, CTL with cost-constrained modalities, is PSPACE-complete (while it has been shown undecidable as soon as the model has three clocks). We also prove that model-checking WMTL, LTL with cost-constrained modalities, is decidable only if there is a single clock in the model and a single stopwatch cost variable (i.e., whose slopes lie in {0,1}).Comment: 28 page

Verification of Broadcasting Multi-Agent Systems against an Epistemic Strategy Logic

We study a class of synchronous, perfect-recall multi-agent systems with imperfect information and broadcasting, i.e., fully observable actions. We define an epistemic extension of strategy logic with incomplete information and the assumption of uniform and coherent strategies. In this setting, we prove that the model checking problem, and thus rational synthesis, is non-elementary decidable. We exemplify the applicability of the framework on a rational secret-sharing scenario

Games with recurring certainty

Infinite games where several players seek to coordinate under imperfect information are known to be intractable, unless the information flow is severely restricted. Examples of undecidable cases typically feature a situation where players become uncertain about the current state of the game, and this uncertainty lasts forever. Here we consider games where the players attain certainty about the current state over and over again along any play. For finite-state games, we note that this kind of recurring certainty implies a stronger condition of periodic certainty, that is, the events of state certainty ultimately occur at uniform, regular intervals. We show that it is decidable whether a given game presents recurring certainty, and that, if so, the problem of synthesising coordination strategies under w-regular winning conditions is solvable.Comment: In Proceedings SR 2014, arXiv:1404.041