A Hennessy-Milner Theorem for ATL with Imperfect Information

Francesco Belardinelli (1) , Catalin Dima (2) , Vadim Malvone (3) , Ferucio Tiplea (4)

1 Imperial College London
2 UPEC UP12 - Université Paris-Est Créteil Val-de-Marne - Paris 12
3 IBISC - Informatique, BioInformatique, Systèmes Complexes
4 UAIC - Alexandru Ioan Cuza University of Iași = Universitatea Alexandru Ioan Cuza din Iași

We show that a history-based variant of alternating bisimulation with imperfect information allows it to be related to a variant of Alternating-time Temporal Logic (ATL) with imperfect information by a full Hennessy-Milner theorem. The variant of ATL we consider has a common knowledge semantics, which requires that the uniform strategy available for a coalition to accomplish some goal must be common knowledge inside the coalition, while other semantic variants of ATL with imperfect information do not accomodate a Hennessy-Milner theorem. We also show that the existence of a history-based alternating bisimulation between two finite Concurrent Game Structures with imperfect information (iCGS) is undecidable.

Mots clés: ATL; Bisimulation; Concurrent Game Structures with Imperfect Information; Gale-Stewart determinacy

Domaines: Informatique et théorie des jeux [cs.GT]

Francesco Belardinelli, Catalin Dima, Vadim Malvone, Ferucio Tiplea. A Hennessy-Milner Theorem for ATL with Imperfect Information. 35th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2020), Jul 2020, Saarbrücken, Germany. pp.181--194, ⟨10.1145/3373718.3394784⟩. ⟨hal-02867538⟩