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.STACS.2016.30
URN: urn:nbn:de:0030-drops-57319
URL: https://drops.dagstuhl.de/opus/volltexte/2016/5731/
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Daviaud, Laure ; Kuperberg, Denis ; Pin, Jean-√Čric

Varieties of Cost Functions

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Abstract

Regular cost functions were introduced as a quantitative generalisation of regular languages, retaining many of their equivalent characterisations and decidability properties. For instance, stabilisation monoids play the same role for cost functions as monoids do for regular languages. The purpose of this article is to further extend this algebraic approach by generalising two results on regular languages to cost functions: Eilenberg's varieties theorem and profinite equational characterisations of lattices of regular languages. This opens interesting new perspectives, but the specificities of cost functions introduce difficulties that prevent these generalisations to be straightforward. In contrast, although syntactic algebras can be defined for formal power series over a commutative ring, no such notion is known for series over semirings and in particular over the tropical semiring.

BibTeX - Entry

@InProceedings{daviaud_et_al:LIPIcs:2016:5731,
  author =	{Laure Daviaud and Denis Kuperberg and Jean-{\'E}ric Pin},
  title =	{{Varieties of Cost Functions}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{30:1--30:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Nicolas Ollinger and Heribert Vollmer},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/5731},
  URN =		{urn:nbn:de:0030-drops-57319},
  doi =		{10.4230/LIPIcs.STACS.2016.30},
  annote =	{Keywords: Cost functions, regular language, varieties, syntactic algebra}
}

Keywords: Cost functions, regular language, varieties, syntactic algebra
Collection: 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)
Issue Date: 2016
Date of publication: 16.02.2016


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