Completeness of the bounded satisfiability problem for constraint LTL

Authors:
Marcello M. Bersani;Achille Frigeri;Matteo Rossi;Pierluigi San Pietro
Affiliations:
Politecnico di Milano;Politecnico di Milano;Politecnico di Milano;Politecnico di Milano
Venue:
RP'11 Proceedings of the 5th international conference on Reachability problems
Year:
2011

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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 δπω, 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.