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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-03334813
Contributor : Benedikt Bollig Connect in order to contact the contributor
Submitted on : Friday, November 26, 2021 - 11:07:01 AM
Last modification on : Tuesday, January 4, 2022 - 6:39:13 AM

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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, Elsevier, 2021, 115, pp.22-53. ⟨10.1016/j.jcss.2020.06.006⟩. ⟨hal-03334813⟩

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