The Shortest Identities for Max-Plus Automata with Two States

Daviaud, Laure; Johnson, Marianne

doi:10.4230/LIPIcs.MFCS.2017.48

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DOI: 10.4230/LIPIcs.MFCS.2017.48
URN: urn:nbn:de:0030-drops-81048

Author Details

Laure Daviaud

Marianne Johnson

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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)
https://doi.org/10.4230/LIPIcs.MFCS.2017.48

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.

Keywords

Max-plus automata
Weighted automata
Identities
Tropical matrices

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References

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