Dependences in Strategy Logic

Patrick Gardy (1) , Patricia Bouyer (2) , Nicolas Markey (3)

1 Shanghai Key Laboratory of Trustworthy Computing
2 LSV - Laboratoire Spécification et Vérification
3 SUMO - SUpervision of large MOdular and distributed systems

Strategy Logic (SL) is a very expressive temporal logic for specifying and verifying properties of multi-agent systems: in SL, one can quantify over strategies, assign them to agents, and express LTL properties of the resulting plays. Such a powerful framework has two drawbacks: first, model checking SL has non-elementary complexity; second, the exact semantics of SL is rather intricate, and may not correspond to what is expected. In this paper, we focus on strategy dependences in SL, by tracking how existentially-quantified strategies in a formula may (or may not) depend on other strategies selected in the formula, revisiting the approach of [Mogavero et al., Reasoning about strategies: On the model-checking problem, 2014]. We explain why elementary dependences, as defined by Mogavero et al., do not exactly capture the intended concept of behavioral strategies. We address this discrepancy by introducing timeline dependences, and exhibit a large fragment of SL for which model checking can be performed in 2-EXPTIME under this new semantics.

Domaines: Informatique [cs]; Logique en informatique [cs.LO]; Informatique et théorie des jeux [cs.GT]

Patrick Gardy, Patricia Bouyer, Nicolas Markey. Dependences in Strategy Logic. Theory of Computing Systems, 2020, 64 (3), pp.467-507. ⟨10.1007/s00224-019-09926-y⟩. ⟨hal-02917561⟩