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On the complexity of resource-bounded logics

Alechina, Natasha; Bulling, Nils; Demri, St�phane; Logan, Brian S.

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Authors

Natasha Alechina

Nils Bulling

St�phane Demri

Brian S. Logan



Abstract

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.

Citation

Alechina, N., Bulling, N., Demri, S., & Logan, B. S. (2018). On the complexity of resource-bounded logics. Theoretical Computer Science, 750, 69-100. https://doi.org/10.1016/j.tcs.2018.01.019

Journal Article Type Article
Acceptance Date Jan 24, 2018
Online Publication Date Feb 2, 2018
Publication Date Nov 30, 2018
Deposit Date Jan 26, 2018
Publicly Available Date Feb 2, 2018
Journal Theoretical Computer Science
Print ISSN 0304-3975
Electronic ISSN 0304-3975
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 750
Pages 69-100
DOI https://doi.org/10.1016/j.tcs.2018.01.019
Public URL https://nottingham-repository.worktribe.com/output/908339
Publisher URL https://www.sciencedirect.com/science/article/pii/S0304397518300665
Contract Date Jan 26, 2018

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