Model-checking for Resource-Bounded ATL with production and consumption of resources

Several logics for expressing coalitional ability under resource bounds have been proposed and studied in the literature. Previous work has shown that if only consumption of resources is considered or the total amount of resources produced or consumed on any path in the system is bounded, then the model-checking problem for several standard logics, such as Resource-Bounded Coalition Logic (RB-CL) and Resource-Bounded Alternating-Time Temporal Logic (RB-ATL) is decidable. However, for coalition logics with unbounded resource production and consumption, only some undecidability results are known. In this paper, we show that the model-checking problem for RB-ATL with unbounded production and consumption of resources is decidable but EXPSPACE-hard. We also investigate some tractable cases and provide a detailed comparison to a variant of the resource logic RAL, together with new complexity results

Model-checking for resource-bounded ATL with production and consumption of resources

Several logics for expressing coalitional ability under resource bounds have been proposed and studied in the literature. Previous work has shown that if only consumption of resources is considered or the total amount of resources produced or consumed on any path in the system is bounded, then the model-checking problem for several standard logics, such as Resource-Bounded Coalition Logic (RB-CL) and Resource-Bounded Alternating-Time Temporal Logic (RB-ATL) is decidable. However, for coalition logics with unbounded resource production and consumption, only some undecidability results are known. In this paper, we show that the modelchecking problem for RB-ATL with unbounded production and consumption of resources is decidable but EXPSPACE-hard. We also investigate some tractable cases and provide a detailed comparison to a variant of the resource logic RAL, together with new complexity results

The virtues of idleness: A decidable fragment of resource agent logic

Alternating Time Temporal Logic (ATL) is widely used for the verification of multi-agent systems. We consider Resource Agent Logic (RAL), which extends ATL to allow the verification of properties of systems where agents act under resource constraints. The model checking problem for RAL with unbounded production and consumption of resources is known to be undecidable. We review existing (un)decidability results for fragments of RAL , tighten some existing undecidability results, and identify several aspects which affect decidability of model checking. One of these aspects is the availability of a ‘do nothing’, or idle action, which does not produce or consume resources. Analysis of undecidability results allows us to identify a significant new fragment of RAL for which model checking is decidable

On the complexity of resource-bounded logics

We revisit decidability results for resource-bounded logics and use decision problems on vector addition systems with states (VASS) in order to establish complexity characterisations of (decidable) model checking problems. We show that the model checking problem for the logic RB+-ATL is 2EXPTIME-complete by using recent results on alternating VASS (and in EXPTIME when the number of resources is bounded). Moreover, we establish that the model checking problem for RBTL is EXPSPACE-complete. The problem is decidable and of the same complexity for RBTL*, proving a new decidability result as a by-product of the approach. When the number of resources is bounded, the problem is in PSPACE. We also establish that the model checking problem for RB+-ATL*, the extension of RB+-ATL with arbitrary path formulae, is decidable by a reduction to parity games for single-sided VASS (a variant of alternating VASS). Furthermore, we are able to synthesise values for resource parameters. Hence, the paper establishes formal correspondences between model checking problems for resource bounded logics advocated in the AI literature and decision problems on alternating VASS, paving the way for more applications and cross-fertilizations