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

Authors: Hans Leiss

Published in: LIPIcs, Volume 62, 25th EACSL Annual Conference on Computer Science Logic (CSL 2016)


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.

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Hans Leiss. The Matrix Ring of a mu-Continuous Chomsky Algebra is mu-Continuous. In 25th EACSL Annual Conference on Computer Science Logic (CSL 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 62, pp. 6:1-6:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)


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@InProceedings{leiss:LIPIcs.CSL.2016.6,
  author =	{Leiss, Hans},
  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 =	{Talbot, Jean-Marc and Regnier, Laurent},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2016.6},
  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}
}
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