City Research Online

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.

Publication Type:	Conference or Workshop Item (Paper)
Additional Information:	© Laure Daviaud, Denis Kuperberg, and Jean-Éric Pin; licensed under Creative Commons License CC-BY
Publisher Keywords:	Cost functions, regular language, varieties, syntactic algebra
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments:	School of Science & Technology > Computer Science

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