Communicating finite-state machines, first-order logic, and star-free propositional dynamic logic

Benedikt Bollig (1, 2) , Marie Fortin (2) , Paul Gastin (1, 2)

1 LMF - Laboratoire Méthodes Formelles
2 LSV - Laboratoire Spécification et Vérification

Message sequence charts (MSCs) naturally arise as executions of communicating finite-state machines (CFMs), in which finite-state processes exchange messages through unbounded FIFO channels. We study the first-order logic of MSCs, featuring Lamport’s happened-before relation. To this end, we introduce a star-free version of propositional dynamic logic (PDL) with loop and converse. Our main results state that (i) every first-order sentence can be transformed into an equivalent star-free PDL sentence (and conversely), and (ii) every star-free PDL sentence can be translated into an equivalent CFM. This answers an open question and settles the exact relation between CFMs and fragments of monadic second-order logic. As a byproduct, we show that first-order logic over MSCs has the three-variable property.

Mots clés: communicating finite-state machines; first-order logic; happened-before relation; propositional dynamic logic

Domaines: Théorie et langage formel [cs.FL]

Benedikt Bollig, Marie Fortin, Paul Gastin. Communicating finite-state machines, first-order logic, and star-free propositional dynamic logic. Journal of Computer and System Sciences, 2021, 115, pp.22-53. ⟨10.1016/j.jcss.2020.06.006⟩. ⟨hal-03334813⟩