Abstract
We consider First-Order Linear Temporal Logic (FO-LTL) over linear time. Inspired by the success of formal approaches based upon finite-model finders, such as Alloy, we focus on finding models with finite first-order domains for FO-LTL formulas, while retaining an infinite time domain. More precisely, we investigate the complexity of the following problem: given a formula \(\varphi \) and an integer n, is there a model of \(\varphi \) with domain of cardinality at most n? We show that depending on the logic considered (FO or FO-LTL) and on the precise encoding of the problem, the problem is either NP-complete, NEXPTIME-complete, PSPACE-complete or EXPSPACE-complete. In a second part, we exhibit cases where the Finite Model Property can be lifted from fragments of FO to their FO-LTL extension.
Research partly funded by ANR/DGA project Cx (ref. ANR-13-ASTR-0006) and by fondation STAE project BRIefcaSE.
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Notes
- 1.
Available at http://alloy.mit.edu/alloy.
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Kuperberg, D., Brunel, J., Chemouil, D. (2016). On Finite Domains in First-Order Linear Temporal Logic. In: Artho, C., Legay, A., Peled, D. (eds) Automated Technology for Verification and Analysis. ATVA 2016. Lecture Notes in Computer Science(), vol 9938. Springer, Cham. https://doi.org/10.1007/978-3-319-46520-3_14
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