Reasoning with a Bounded Number of Resources in ATL+

Francesco Belardinelli (1) , Stéphane Demri (2, 3)

1 Imperial College London
2 CNRS - Centre National de la Recherche Scientifique
3 LSV - Laboratoire Spécification et Vérification [Cachan]

The resource-bounded alternating-time temporal logic RB±ATL combines strategic reasoning with reasoning about resources. Its model-checking problem is known to be 2EXPTIME-complete (the same as its proper extension RB±ATL *). Several fragments have been identified to lower the complexity. In this work, we consider the variant RB±ATL + which permits Boolean combinations of path formulae starting with single temporal operators, but restricted to a single resource, providing an interesting trade-off between temporal expressivity and resource analysis. We show that the model-checking problem for RB±ATL + restricted to a single agent and a single resource is ∆p2-complete, hence the same as for CTL +. In this case reasoning about resources comes at no extra computational cost. Furthermore, we show that, with an arbitrary number of agents and a fixed number of resources, the problem can be solved in EXPTIME using a Turing reduction to the parity game problem for alternating vector addition systems with states.

Mots clés: model-checking algorithm; 2EXPTIME; translation; alternating-time temporal logic ATL; resource; alternating-time temporal logic ATL+; model-checking; one resource; resource-bounded concurrent game structure; bounded number of resources; complexity; alternating vector addition system (AVASS); vector addition system (VAS)

Domaines: Informatique [cs]; Logique en informatique [cs.LO]; Intelligence artificielle [cs.AI]

Francesco Belardinelli, Stéphane Demri. Reasoning with a Bounded Number of Resources in ATL+. 24th European Conference on Artificial Intelligence, Aug 2020, Santiago de Compostela, Spain. pp.624--631, ⟨10.3233/FAIA200147⟩. ⟨hal-03005853⟩