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DOI: 10.4230/LIPIcs.MFCS.2017.48
The Shortest Identities for Max-Plus Automata with Two States

Authors: Laure Daviaud and Marianne Johnson

Published in: LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

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.
Cite as

Laure Daviaud and Marianne Johnson. The Shortest Identities for Max-Plus Automata with Two States. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 48:1-48:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{daviaud_et_al:LIPIcs.MFCS.2017.48,
  author =	{Daviaud, Laure and Johnson, Marianne},
  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 =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.48},
  URN =		{urn:nbn:de:0030-drops-81048},
  doi =		{10.4230/LIPIcs.MFCS.2017.48},
  annote =	{Keywords: Max-plus automata, Weighted automata, Identities, Tropical matrices}
}
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