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.ICALP.2019.129
URN: urn:nbn:de:0030-drops-107056
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10705/
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Schmitz, Sylvain

The Parametric Complexity of Lossy Counter Machines

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LIPIcs-ICALP-2019-129.pdf (0.6 MB)

Abstract

The reachability problem in lossy counter machines is the best-known ACKERMANN-complete problem and has been used to establish most of the ACKERMANN-hardness statements in the literature. This hides however a complexity gap when the number of counters is fixed. We close this gap and prove F_d-completeness for machines with d counters, which provides the first known uncontrived problems complete for the fast-growing complexity classes at levels 3 < d < omega. We develop for this an approach through antichain factorisations of bad sequences and analysing the length of controlled antichains.

BibTeX - Entry

@InProceedings{schmitz:LIPIcs:2019:10705,
  author =	{Sylvain Schmitz},
  title =	{{The Parametric Complexity of Lossy Counter Machines}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{129:1--129:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10705},
  URN =		{urn:nbn:de:0030-drops-107056},
  doi =		{10.4230/LIPIcs.ICALP.2019.129},
  annote =	{Keywords: Counter machine, well-structured system, well-quasi-order, antichain, fast-growing complexity}
}

Keywords: Counter machine, well-structured system, well-quasi-order, antichain, fast-growing complexity
Collection: 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)
Issue Date: 2019
Date of publication: 04.07.2019

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