We introduce the notion of ideal, prime ideal, lter, fuzzy ideal, fuzzy prime ideal, fuzzy lter of ordered $Gamma$-semiring and study their properties and relations between them. We characterize the prime ideals and lters of ordered $Gamma$-semiring with respect to fuzzy ideals and fuzzy l- ters respectively.

We consider tree automata with costs over semirings in the sense of (Seidl, 1994). We define the concept of a finitely factorizing semiring and of a monotonic semiring, both as the generalization of well-known particular semirings, and show that the costfiniteness of tree automata with costs over finitely factorizing and monotonic semirings is decidable. We show that, for tree automata with cos...

We consider tree automata with costs over semirings in the sense of (Seidl, 1994). We de ne the concept of a nitely factorizing semiring and of a monotonic semiring, both as the generalization of well-known particular semirings, and show that the costniteness of tree automata with costs over nitely factorizing and monotonic semirings is decidable. We show that, for tree automata with costs over...

Distributed trust management supports the provision of the required levels in a flexible and scalable manner by locally discriminating between the entities with which a principal should interact. However, there is a tension between the preservation of privacy and the controlled release of information when an entity submits credentials for establishing and verifying trust metric where it may dis...

The notion of a &Gamma-semigroup was introduced by Sen [8] in 1981. We can see that any semigroup can be considered as a &Gamma-semigroup. The aim of this article is to study the concept of (0-)minimal and max- imal ordered bi-ideals in ordered &Gamma-semigroups, and give some charac- terizations of (0-)minimal and maximal ordered bi-ideals in ordered &Gamma- semigroups analogous to the charact...

A semiring can be “completed” (i.e., embedded into a semiring in which all infinite sums are defined and satisfy some reasonable properties) iff this semiring can be naturally partially ordered. This construction is “natural” (a left adjoint to the forgetful functor), and quite straightforward. Definitions and easy facts Definition 1. A semiring is a structure (S,+, ·, 0, 1) such that (S,+, 0) ...

For several semirings S, two weighted finite automata with multiplicities in S are equivalent if and only if they can be connected by a chain of simulations. Such a semiring S is called “proper”. It is known that the Boolean semiring, the semiring of natural numbers, the ring of integers, all finite commutative positively ordered semirings and all fields are proper. The semiring S is Noetherian...

We consider rational power series over an alphabet Σ 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 prefixed point rule and/or its dual. The results are generalizations of Kozen’s axiomatization of regular languages.