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.MFCS.2017.48
URN: urn:nbn:de:0030-drops-81048
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/8104/
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Daviaud, Laure ; Johnson, Marianne

The Shortest Identities for Max-Plus Automata with Two States

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Abstract

Max-plus automata are quantitative extensions of automata designed to associate an integer with every non-empty word. A pair of distinct words is said to be an identity for a class of max-plus automata if each of the automata in the class computes the same value on the two words. We give the shortest identities holding for the class of max-plus automata with two states. For this, we exhibit an interesting list of necessary conditions for an identity to hold. Moreover, this result provides a counter-example of a conjecture of Izhakian, concerning the minimality of certain identities.

BibTeX - Entry

@InProceedings{daviaud_et_al:LIPIcs:2017:8104,
  author =	{Laure Daviaud and Marianne Johnson},
  title =	{{The Shortest Identities for Max-Plus Automata with Two States}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{48:1--48:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Kim G. Larsen and Hans L. Bodlaender and Jean-Francois Raskin},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8104},
  URN =		{urn:nbn:de:0030-drops-81048},
  doi =		{10.4230/LIPIcs.MFCS.2017.48},
  annote =	{Keywords: Max-plus automata, Weighted automata, Identities, Tropical matrices}
}

Keywords: Max-plus automata, Weighted automata, Identities, Tropical matrices
Collection: 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)
Issue Date: 2017
Date of publication: 01.12.2017

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