Bollig, Benedikt ;
Fortin, Marie ;
Gastin, Paul
It Is Easy to Be Wise After the Event: Communicating Finite-State Machines Capture First-Order Logic with "Happened Before"
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. 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.
BibTeX - Entry
@InProceedings{bollig_et_al:LIPIcs:2018:9545,
author = {Benedikt Bollig and Marie Fortin and Paul Gastin},
title = {{It Is Easy to Be Wise After the Event: Communicating Finite-State Machines Capture First-Order Logic with "Happened Before"}},
booktitle = {29th International Conference on Concurrency Theory (CONCUR 2018)},
pages = {7:1--7:17},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-087-3},
ISSN = {1868-8969},
year = {2018},
volume = {118},
editor = {Sven Schewe and Lijun Zhang},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2018/9545},
URN = {urn:nbn:de:0030-drops-95455},
doi = {10.4230/LIPIcs.CONCUR.2018.7},
annote = {Keywords: communicating finite-state machines, first-order logic, happened-before relation}
}
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Keywords: |
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communicating finite-state machines, first-order logic, happened-before relation |
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Seminar: |
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29th International Conference on Concurrency Theory (CONCUR 2018)
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Issue date: |
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2018 |
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Date of publication: |
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2018 |
2018
