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 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.
Highlights
Alternating-Time Temporal Logic (ATL) [1] is widely used in verification of multi-agent systems
ATL can express properties related to coalitional ability, for example, one can state that a group of agents A has a strategy such that whatever the actions by the agents outside the coalition, any computation of the system generated by the strategy satisfies some temporal property
In the case of fully observable models and memoryless agents, the model-checking problem for ATL is polynomial in the size of the model and the formula, while it is undecidable for partially observable models where agents have perfect recall [2]
Summary
Alternating-Time Temporal Logic (ATL) [1] is widely used in verification of multi-agent systems. Both until-strategy and box-strategy take a search tree node n and a formula φ ∈ Sub(φ0) as input, and have similar structure They first check if the infinite resource version of φ (i.e., φ where the outermost coalition modality has bound ∞ ̄ ). (Note that the state represented by n has already been labelled by the resource bounded subformulas φ and ψ .) If so, they return false immediately, terminating search of the current branch of the search tree (lines 2–3 of Algorithms 2 and 3). The existence of the latter subsequence would constitute a contradiction, because comparable resource availability vectors for nodes with the same state will lead to termination after finitely many steps (so there cannot be an infinite sequence of recursive calls) To see why this is so, consider the simpler case of box-strategy first. If box-strategy(node0(s, b), Ab 2φ) returns false s |= Ab 2φ
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