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.

Completeness of the Bounded Satisfiability Problem for Constraint LTL.

BERSANI, MARCELLO MARIA;FRIGERI, ACHILLE;ROSSI, MATTEO GIOVANNI;SAN PIETRO, PIERLUIGI
2011

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.
5th International Workshop on Reachability Problems, RP 2011
9783642242878
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/635439
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