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.2017.16
URN: urn:nbn:de:0030-drops-84033
URL: https://drops.dagstuhl.de/opus/volltexte/2018/8403/
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Blondin, Michael ; Finkel, Alain ; Goubault-Larrecq, Jean

Forward Analysis for WSTS, Part III: Karp-Miller Trees

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Abstract

This paper is a sequel of "Forward Analysis for WSTS, Part I: Completions" [STACS 2009, LZI Intl. Proc. in Informatics 3, 433–444] and "Forward Analysis for WSTS, Part II: Complete WSTS" [Logical Methods in Computer Science 8(3), 2012]. In these two papers, we provided a framework to conduct forward reachability analyses of WSTS, using finite representations of downwards-closed sets. We further develop this framework to obtain a generic Karp-Miller algorithm for the new class of very-WSTS. This allows us to show that coverability sets of very-WSTS can be computed as their finite ideal decompositions. Under natural assumptions on positive sequences, we also show that LTL model checking for very-WSTS is decidable. The termination of our procedure rests on a new notion of acceleration levels, which we study. We characterize those domains that allow for only finitely many accelerations, based on ordinal ranks.

BibTeX - Entry

@InProceedings{blondin_et_al:LIPIcs:2018:8403,
  author =	{Michael Blondin and Alain Finkel and Jean Goubault-Larrecq},
  title =	{{Forward Analysis for WSTS, Part III: Karp-Miller Trees}},
  booktitle =	{37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)},
  pages =	{16:1--16:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-055-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{93},
  editor =	{Satya Lokam and R. Ramanujam},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8403},
  URN =		{urn:nbn:de:0030-drops-84033},
  doi =		{10.4230/LIPIcs.FSTTCS.2017.16},
  annote =	{Keywords: WSTS, model checking, coverability, Karp-Miller algorithm, ideals}
}

Keywords: WSTS, model checking, coverability, Karp-Miller algorithm, ideals
Collection: 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)
Issue Date: 2018
Date of publication: 12.02.2018

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