Free inductive K-semialgebras
arXiv:1009.4820
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.