eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-08-31
7:1
7:17
10.4230/LIPIcs.CONCUR.2018.7
article
It Is Easy to Be Wise After the Event: Communicating Finite-State Machines Capture First-Order Logic with "Happened Before"
Bollig, Benedikt
1
Fortin, Marie
1
Gastin, Paul
1
LSV, CNRS & ENS Paris-Saclay, Université Paris-Saclay, Cachan, France
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol118-concur2018/LIPIcs.CONCUR.2018.7/LIPIcs.CONCUR.2018.7.pdf
communicating finite-state machines
first-order logic
happened-before relation