Abstract
We show that the satisfiability problem for LTL (with past operators) over arithmetic constraints (Constraint LTL) can be answered by solving a finite amount of instances of bounded satisfiability problems when atomic formulae belong to certain suitable fragments of Presburger arithmetic. A formula is boundedly satisfiable when it admits an ultimately periodic model of the form δπ ω, where δ and π are finite sequences of symbolic valuations. Therefore, for every formula there exists a completeness bound c, such that, if there is no ultimately periodic model with |δπ| ≤ c, then the formula is unsatisfiable.
This research was partially supported by Programme IDEAS-ERC and Project 227977-SMScom.
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Bersani, M.M., Frigeri, A., Rossi, M., San Pietro, P. (2011). Completeness of the Bounded Satisfiability Problem for Constraint LTL. In: Delzanno, G., Potapov, I. (eds) Reachability Problems. RP 2011. Lecture Notes in Computer Science, vol 6945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24288-5_7
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DOI: https://doi.org/10.1007/978-3-642-24288-5_7
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