Technical Report: Model-Checking for Resource-Bounded ATL with Production and Consumption of Resources

TL;DR

This paper proves that model-checking for RB-ATL with unbounded resource production and consumption is decidable and EXPSPACE-hard, exploring tractable cases and comparing with related resource logics.

Contribution

It establishes decidability and complexity results for RB-ATL with unbounded resources, a previously unresolved issue in the field.

Findings

Model-checking for RB-ATL with unbounded resources is decidable.

The problem is EXPSPACE-hard.

Certain cases are identified as tractable.

Abstract

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 con- sumption 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.