Strategic reasoning with a bounded number of resources: The quest for tractability

Abstract

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 * ) and fragments have been identified to lower the complexity.In this work, we consider the variant RB±ATL + that allows for 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 ∆ P 2 -complete, hence the same as for the standard branching-time temporal logic CTL + . In this case reasoning about resources comes at no extra computational cost. When a fixed finite set of linear-time temporal operators is considered, the model-checking problem drops to ptime, which includes the special case of RB±ATL restricted to a single agent and a single resource. Furthermore, we show that, with an arbitrary number of agents and a fixed number of resources, the model-checking problem for RB±ATL + can be solved in exptime using a sophisticated Turing reduction to the parity game problem for alternating vector addition systems with states (AVASS).