License: Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2019.48
URN: urn:nbn:de:0030-drops-116107
URL: https://drops.dagstuhl.de/opus/volltexte/2019/11610/
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Mansard, Alexandre

Boolean Algebras from Trace Automata

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LIPIcs-FSTTCS-2019-48.pdf (0.7 MB)


Abstract

We consider trace automata. Their vertices are Mazurkiewicz traces and they accept finite words. Considering the length of a trace as the length of its Foata normal form, we define the operations of level-length synchronization and of superposition of trace automata. We show that if a family F of trace automata is closed under these operations, then for any deterministic automaton H in F, the word languages accepted by the deterministic automata of F that are length-reducible to H form a Boolean algebra. We show that the family of trace suffix automata with level-regular contexts and the subfamily of vector addition systems satisfy these closure properties. In particular, this yields various Boolean algebras of word languages accepted by deterministic vector addition systems.

BibTeX - Entry

@InProceedings{mansard:LIPIcs:2019:11610,
  author =	{Alexandre Mansard},
  title =	{{Boolean Algebras from Trace Automata}},
  booktitle =	{39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)},
  pages =	{48:1--48:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-131-3},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{150},
  editor =	{Arkadev Chattopadhyay and Paul Gastin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2019/11610},
  URN =		{urn:nbn:de:0030-drops-116107},
  doi =		{10.4230/LIPIcs.FSTTCS.2019.48},
  annote =	{Keywords: Boolean algebras, traces, automata, synchronization, pushdown automata, vector addition systems}
}

Keywords: Boolean algebras, traces, automata, synchronization, pushdown automata, vector addition systems
Collection: 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)
Issue Date: 2019
Date of publication: 04.12.2019


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