License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CONCUR.2022.28
URN: urn:nbn:de:0030-drops-170915
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17091/
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Adsul, Bharat ; Gastin, Paul ; Sarkar, Saptarshi ; Weil, Pascal

Propositional Dynamic Logic and Asynchronous Cascade Decompositions for Regular Trace Languages

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LIPIcs-CONCUR-2022-28.pdf (0.8 MB)

Abstract

One of the main motivations for this work is to obtain a distributed Krohn-Rhodes theorem for Mazurkiewicz traces. Concretely, we focus on the recently introduced operation of local cascade product of asynchronous automata and ask if every regular trace language can be accepted by a local cascade product of "simple" asynchronous automata.
Our approach crucially relies on the development of a local and past-oriented propositional dynamic logic (LocPastPDL) over traces which is shown to be expressively complete with respect to all regular trace languages. An event-formula of LocPastPDL allows to reason about the causal past of an event and a path-formula of LocPastPDL, localized at a process, allows to march along the sequence of past-events in which that process participates, checking for local regular patterns interspersed with local tests of other event-formulas. We also use additional constant formulas to compare the leading process events from the causal past. The new logic LocPastPDL is of independent interest, and the proof of its expressive completeness is rather subtle.
Finally, we provide a translation of LocPastPDL formulas into local cascade products. More precisely, we show that every LocPastPDL formula can be computed by a restricted local cascade product of the gossip automaton and localized 2-state asynchronous reset automata and localized asynchronous permutation automata.

BibTeX - Entry

@InProceedings{adsul_et_al:LIPIcs.CONCUR.2022.28,
  author =	{Adsul, Bharat and Gastin, Paul and Sarkar, Saptarshi and Weil, Pascal},
  title =	{{Propositional Dynamic Logic and Asynchronous Cascade Decompositions for Regular Trace Languages}},
  booktitle =	{33rd International Conference on Concurrency Theory (CONCUR 2022)},
  pages =	{28:1--28:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-246-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{243},
  editor =	{Klin, Bartek and Lasota, S{\l}awomir and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17091},
  URN =		{urn:nbn:de:0030-drops-170915},
  doi =		{10.4230/LIPIcs.CONCUR.2022.28},
  annote =	{Keywords: Mazurkiewicz traces, propositional dynamic logic, regular trace languages, asynchronous automata, cascade product, Krohn Rhodes theorem}
}

Keywords: Mazurkiewicz traces, propositional dynamic logic, regular trace languages, asynchronous automata, cascade product, Krohn Rhodes theorem
Collection: 33rd International Conference on Concurrency Theory (CONCUR 2022)
Issue Date: 2022
Date of publication: 06.09.2022

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