Hodkinson, I.M. and Kontchakov, Roman and Kurucz, A. and Wolter, F. and Zakharyaschev, Michael (2003) On the computational complexity of decidable fragments of first-order linear temporal logics. In: UNSPECIFIED (ed.) 10th International Symposium on Temporal Representation and Reasoning. IEEE Computer Society, pp. 91-98. ISBN 0769519121.
Abstract
We study the complexity of some fragments of first-order temporal logic over natural numbers time. The one-variable fragment of linear first-order temporal logic even with sole temporal operator /spl square/ is EXPSPACE-complete (this solves an open problem of J. Halpern and M. Vardi (1989)). So are the one-variable, two-variable and monadic monodic fragments with Until and Since. If we add the operators O/sup n/, with n given in binary, the fragment becomes 2EXPSPACE-complete. The packed monodic fragment has the same complexity as its pure first-order part - 2EXPTIME-complete. Over any class of flows of time containing one with an infinite ascending sequence - e.g., rationals and real numbers time, and arbitrary strict linear orders - we obtain EXPSPACE lower bounds (which solves an open problem of M. Reynolds (1997)). Our results continue to hold if we restrict to models with finite first-order domains.
Metadata
| Item Type: | Book Section |
|---|---|
| School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Sarah Hall |
| Date Deposited: | 11 May 2021 18:39 |
| Last Modified: | 09 Aug 2023 12:50 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/44230 |
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