Free inductive K-semialgebras

Details Free inductive K-semialgebras Free inductive K-semialgebras

2010-09-24

arxiv.org/abs/1009.4820v2

Computer Science

Formal Languages and Automata Theory

Scientific paper

We consider rational power series over an alphabet $\Sigma$ with coefficients
in a ordered commutative semiring $K$ and characterize them as the free ordered
$K$-semialgebras in various classes of ordered $K$-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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