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

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 μcontinuous 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 μ. We prove that the matrix ring of a μ-continuous Chomsky algebra also is a μ-continuous Chomsky algebra. 1998 ACM Subject Classification F 4.3 Formal languages, F 4.2 Grammars and Other Rewriting Systems, D 3.3 Language Constructs, F.3.3 Studies of Program Constructs

DOI: 10.4230/LIPIcs.CSL.2016.6

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Cite this paper

@inproceedings{Leiss2016TheMR, title={The Matrix Ring of a μ-Continuous Chomsky Algebra is mu-Continuous}, author={Hans Leiss}, booktitle={CSL}, year={2016} }