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

Author Hans Leiss

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Hans Leiss

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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)
https://doi.org/10.4230/LIPIcs.CSL.2016.6

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.
Keywords
  • context-free language
  • fixed point operator
  • idempotent semiring
  • matrix ring
  • Chomsky algebra

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