Article ID Journal Published Year Pages File Type
396110 Information Sciences 2007 12 Pages PDF
Abstract

A ∗–λ-semiring is an ordered semiring S equipped with a star operation such that for any a, b ∈ S, a∗b is the least fixed point of the linear mapping x ↦ ax + b over S. The notion of ∗–λ-semirings is a generalization of several important concepts such as continuous semirings, (weak) inductive ∗-semirings and the Kleene algebras of Conway and Kozen. We investigate several basic properties of ∗–λ-semirings and obtain results on ∗–λ-semirings in relation to preorders, duality and formal power series. Some of these results can be seen as generalizations of relevant results on inductive ∗-semirings.

Related Topics
Physical Sciences and Engineering Computer Science Artificial Intelligence
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