On the complexity of resource-bounded logics

Alechina, Natasha; Bulling, Nils; Demri, Stéphane; Logan, Brian

doi:10.1016/j.tcs.2018.01.019

Cited by 10 publications

(55 citation statements)

References 16 publications

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“…Remarkably, the number of locations in the target AVASS is exponential in the input size, which makes a substantial difference w.r.t. what is done in [12] for RB±ATL * , where the number of locations is double exponential. Hence, the model-checking problem for RB±ATL + restricted to one resource is pspace-hard (inherited from ATL + [27,28]) and in exptime.…”

Section: Introductionmentioning

confidence: 96%

“…However, if logics for strategies are to be applied to concrete AI scenarios, it is key to account for the resources that actions might consume or produce. These considerations have prompted recently investigations in resource-aware logics for strategies [11,12]. The need for managing resources in MAS has been identified quite early and many logical formalisms based on ATL have been introduced to endow actions with consumption or production of resources [13,14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

“…The logic RB±ATL is a resource-aware logical formalism that extends ATL by endowing actions with the consumption and production of resources [16]. In [12], its model-checking problem is shown 2exptime-complete by using subroutines to solve decision problems for alternating vector addition systems with states (AVASS), see e.g., [21,22,23]. The 2exptime-completeness has also been extended to RB±ATL * , the extension of RB±ATL in which path formulae are arbitrary LTL formulae, in the same way as the temporal logic CTL * extends CTL (see [24,Chapter 7]).…”

Section: Introductionmentioning

confidence: 99%

“…Our motivation for the present contribution is threefold. Firstly, in the literature there are several gaps in the results available for the decidability and complexity related to the 2 model-checking problem for RB±ATL [12]. For instance, if we assume two resources and two agents in our multi-agent systems, then the model-checking problem for RB±ATL is known to be pspace-hard [29] and in exptime [12,Cor.…”

Section: Introductionmentioning

confidence: 99%

“…Our contribution. Based on the logics RB±ATL and RB±ATL * studied in [12] and for which the respective model-checking problems are 2exptime-complete, we identify tractable fragments and lower the worst-case complexity for other fragments. Details follow.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Belardinelli

Demri

2021

Artificial Intelligence

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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).

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Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Belardinelli

Demri

2021

Artificial Intelligence

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Fields of Logic and Computation III

Vovk

2020

Lecture Notes in Computer Science

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Approaches to the verification of multi-agent systems are typically based on games or transition systems defined in terms of states and actions. However such approaches often ignore a key aspect of multi-agent systems, namely that the agents' actions require (and sometimes produce) resources. We survey previous work on the verification of multi-agent systems that takes resources into account, extending substantially a survey from 2016 [9].

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