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.CSL.2016.6
URN: urn:nbn:de:0030-drops-65467
URL: https://drops.dagstuhl.de/opus/volltexte/2016/6546/
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Leiss, Hans

The Matrix Ring of a mu-Continuous Chomsky Algebra is mu-Continuous

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LIPIcs-CSL-2016-6.pdf (0.5 MB)

Abstract

In the course of providing an (infinitary) axiomatization of the equational theory of the class of context-free languages, Grathwohl, Kozen and Henglein (2013) have introduced the class of mu-continuous Chomsky algebras. These are idempotent semirings where least solutions for systems of polynomial inequations (i.e. context-free grammars) can be computed iteratively and where multiplication is continuous with respect to the least fixed point operator mu. We prove that the matrix ring of a mu-continuous Chomsky algebra also is a mu-continuous Chomsky algebra.

BibTeX - Entry

@InProceedings{leiss:LIPIcs:2016:6546,
  author =	{Hans Leiss},
  title =	{{The Matrix Ring of a mu-Continuous Chomsky Algebra is mu-Continuous}},
  booktitle =	{25th EACSL Annual Conference on Computer Science Logic (CSL 2016)},
  pages =	{6:1--6:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-022-4},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{62},
  editor =	{Jean-Marc Talbot and Laurent Regnier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2016/6546},
  URN =		{urn:nbn:de:0030-drops-65467},
  doi =		{10.4230/LIPIcs.CSL.2016.6},
  annote =	{Keywords: context-free language, fixed point operator, idempotent semiring, matrix ring, Chomsky algebra}
}

Keywords: context-free language, fixed point operator, idempotent semiring, matrix ring, Chomsky algebra
Collection: 25th EACSL Annual Conference on Computer Science Logic (CSL 2016)
Issue Date: 2016
Date of publication: 29.08.2016

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