It Is Easy to Be Wise After the Event: Communicating Finite-State Machines Capture First-Order Logic with "Happened Before"

Authors Benedikt Bollig, Marie Fortin, Paul Gastin

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Benedikt Bollig
  • LSV, CNRS & ENS Paris-Saclay, Université Paris-Saclay, Cachan, France
Marie Fortin
  • LSV, CNRS & ENS Paris-Saclay, Université Paris-Saclay, Cachan, France
Paul Gastin
  • LSV, CNRS & ENS Paris-Saclay, Université Paris-Saclay, Cachan, France

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Benedikt Bollig, Marie Fortin, and Paul Gastin. It Is Easy to Be Wise After the Event: Communicating Finite-State Machines Capture First-Order Logic with "Happened Before". In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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. 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • communicating finite-state machines
  • first-order logic
  • happened-before relation


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