Resource-bounded ATL: the Quest for Tractable Fragments
Résumé
Resource-aware logics to represent strategic abilities in multi-agent systems are notoriously hard to handle as they combine strategic reasoning with reasoning about resources. In this work, we begin by providing a general overview of the model-checking results currently available for the Resource-bounded Alternating-timeTemporal Logic RB±ATL. This allows us to identify several open problems in the literature, as well as to establish relationships with RBTL-like logics, when RB±ATL is restricted to a single agent. Then,we tackle one such open problem that we deem highly significant: we show that model-checking RB±ATL is ptime-complete when restricted to a single agent and a single resource. To do so, we make a valuable detour on vector addition systems with states, by proving new complexity results for their statereachability and nontermination problems, when restricted to a single counter. Thus, reasoning about resources comes at no computational extra cost int he single-resource, single-agent case.
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