Specification and Verification of Multi-Agent Systems

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.

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“…In this section we provide an overview of the relevant variants of ATL. We refer the to [3,31,29,6,19] for details.…”

Section: Verifying Strategic Abilitymentioning

confidence: 99%

Approximate verification of strategic abilities under imperfect information

Jamroga

Knapik

Kurpiewski

et al. 2019

Artificial Intelligence

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“…However, difficulties in obtaining a satisfactory formalisation of rational mental states led researchers to seek alternative foundations for modelling rational action in multi-agent systems, and game theory became increasingly adopted as a foundation. See, e.g., [39] for an excellent survey of this stream of work. Of this body of work, it is worth identifying several threads of research that are related to the present paper.…”

Section: Related Workmentioning

confidence: 99%

From model checking to equilibrium checking: Reactive modules for rational verification

Wooldridge

Gutiérrez

Harrenstein

et al. 2017

Artificial Intelligence

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Model checking is the best-known and most successful approach to formally verifying that systems satisfy specifications, expressed as temporal logic formulae. In this article, we develop the theory of equilibrium checking, a related but distinct problem. Equilibrium checking is relevant for multi-agent systems in which system components (agents) are assumed to be acting rationally in pursuit of delegated goals, and is concerned with understanding what temporal properties hold of such systems under the assumption that agents select strategies in equilibrium. The formal framework we use to study this problem assumes agents are modelled using REACTIVE MODULES, a system modelling language that is used in a range of practical model checking systems. Each agent (or player) in a REACTIVE MODULES game is specified as a nondeterministic guarded command program, and each player's goal is specified with a temporal logic formula that the player desires to see satisfied. A strategy for a player in a REACTIVE MODULES game defines how that player selects enabled guarded commands for execution over successive rounds of the game. For this general setting, we investigate games in which players have goals specified in Linear Temporal Logic (in which case it is assumed that players choose deterministic strategies) and in Computation Tree Logic (in which case players select nondeterministic strategies). For each of these cases, after formally defining the game setting, we characterise the complexity of a range of problems relating to Nash equilibria (e.g., the computation or the verification of existence of a Nash equilibrium or checking whether a given temporal formula is satisfied on some Nash equilibrium). We then go on to show how the model we present can be used to encode, for example, games in which the choices available to players are specified using STRIPS planning operators.

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“…In the multi-agent system domain, formalisms for strategic reasoning have assumed a prominent role in the specification, verification, and synthesis tasks [3,[12][13][14][15][16][17]27,29,31]. A story of success in this field is Alternating Temporal Logic (ATL , for short), introduced by Alur, Henzinger, and Kupferman [3].…”

Section: Introductionmentioning

confidence: 99%

A Behavioral Hierarchy of Strategy Logic

Mogavero

Murano

Sauro

2014

Lecture Notes in Computer Science

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Abstract. Starting from the seminal work introducing Alternating Temporal Logic, formalisms for strategic reasoning have assumed a prominent role in multi-agent systems verification. Among the others, Strategy Logic (SL) allows to represent sophisticated solution concepts, by treating agent strategies as first-order objects. A drawback from the high power of SL is to admit non-behavioral strategies: a choice of an agent, at a given point of a play, may depend on choices other agents can make in the future or in counterfactual plays. As the latter moves are unpredictable, such strategies cannot be easily implemented, making the use of the logic problematic in practice. In this paper, we describe a hierarchy of SL fragments as syntactic restrictions of the recently defined Boolean-Goal Strategy Logic (SL[bg]). Specifically, we introduce Alternating-Goal Strategy Logic (SL [ag]) that, by imposing a suitable alternation over the nesting of the Boolean connectives in SL[bg], induces two dual chains of sets of formulas, the conjunctive and disjunctive ones. A formula belongs to the level i of the conjunctive chain if it just contains conjunctions of atomic goals together with a unique formula belonging to the disjunctive chain of level i − 1. The disjunctive chain is defined similarly. We formally prove that classic and behavioral semantics for SL [ag] coincide. Additionally, we study the related model-checking problem showing that it is 2ExpTime-complete.

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Specification and Verification of Multi-Agent Systems

Cited by 16 publications

References 61 publications

Approximate verification of strategic abilities under imperfect information

Approximate verification of strategic abilities under imperfect information

From model checking to equilibrium checking: Reactive modules for rational verification

A Behavioral Hierarchy of Strategy Logic

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