Free inductive K-semialgebras
Zoltan Esik, Werner Kuich
TL;DR
This paper characterizes rational power series over an alphabet with coefficients in an ordered semiring as free ordered K-semialgebras, generalizing Kozen's axiomatization of regular languages.
Contribution
It introduces a new algebraic framework for rational power series using free ordered K-semialgebras with star operations, extending previous axiomatizations.
Findings
Provides a characterization of rational power series as free ordered K-semialgebras
Generalizes Kozen's axiomatization of regular languages
Establishes algebraic structures satisfying least pre-fixed point rules
Abstract
We consider rational power series over an alphabet with coefficients in a ordered commutative semiring and characterize them as the free ordered -semialgebras in various classes of ordered -semialgebras equipped with a star operation satisfying the least pre-fixed point rule and/or its dual. The results are generalizations of Kozen's axiomatization of regular languages.
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Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Logic, programming, and type systems