On the complexity of resource-bounded logics

Alechina, N. and Bulling, N. and Demri, S. and Logan, B. (2018) On the complexity of resource-bounded logics. Theoretical Computer Science . ISSN 0304-3975

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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.

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Computer Science
Identification Number: 10.1016/j.tcs.2018.01.019
Depositing User: Eprints, Support
Date Deposited: 26 Jan 2018 12:02
Last Modified: 24 Feb 2018 17:58
URI: http://eprints.nottingham.ac.uk/id/eprint/49359

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