A Backward-traversal-based Approach for Symbolic Model Checking of Uniform Strategies for Constrained Reachability

Abstract

Since the introduction of Alternating-time Temporal Logic (AT L), many logics have been proposed to reason about different strategic capabilities of the agents of a system. In particular, some logics have been designed to reason about the uniform memoryless strategies of such agents. These strategies are the ones the agents can effectively play by only looking at what they observe from the current state. AT L ir can be seen as the core logic to reason about such uniform strategies. Nevertheless, its model-checking problem is difficult-it requires a polynomial number of calls to an NP oracle-, and practical algorithms to solve it appeared only recently.This paper proposes a technique for model checking uniform memoryless strategies. Existing techniques build the strategies from the states of interest-such as the initial states-through a forward traversal of the system. On the other hand, the proposed approach builds the winning strategies from the target states through a backward traversal, making sure that only uniform strategies are explored. Nevertheless, building the strategies from the ground up limits its applicability to constrained reachability objectives only. This paper describes the approach in details and compares it experimentally with existing approaches implemented into a BDD-based framework. These experiments show that the technique is competitive on the cases it can handle. * This research is financed by the Walloon Region as part of the Logistics in Wallonia competitiveness pole. 1 A ∆ P 2 problem requires a polynomial number of calls to an NP oracle.

Pretty Good Strategies and Where to Find Them

“…That makes incremental synthesis of strategies impossible, or at least difficult to achieve. Some practical attempts to overcome the barrier have been reported in [14,15,16,28,42,33,35]. Up until now, experimental results confirm that the initial intuition was right: model checking of strategic modalities for imperfect information is hard, and dealing with it requires innovative algorithms and verification techniques.…”

“…It means that the procedure will return some strategy even for models whose size is beyond grasp for optimal model checking algorithms. This is a clear advantage over the existing approaches [38,37,16,14,43,33,35] where the algorithms typically provide no output even for relatively small models.…”

“…A prototype tool SMC [43] employs bounded unfoldings of transition relation with strategy exploration and calls to MCMAS. Strategy search with optimisation of partial strategies has been further used in [16,14,35]. Most relevant to us, the optimisation in [35] was driven by strategic dominance based on the tightness of the outcome set.…”

Multi-valued Verification of Strategic Ability

“…Accordingly, the translation in Section 5.1 reduces the problem to model checking of 2-valued ATL with imperfect information. Since the exact model checking of abilities under imperfect information is hard, both theoretically [44,66] and in practice [9,67,57], we go around the complexity by using the fixpoint-based approximate model checking algorithm proposed recently in [63]. That is, the 2valued model checking of ϕ 1R proceeds by a model-independent translation to its upper and lower variants ϕ U 1R , ϕ L 1R , both of which can be verified by fixpoint algorithms.…”