Fixed point equations x = F (x) over ω-continuous semirings are a natural mathematical foundation of interprocedural program analysis. Equations over the semiring of the real numbers can be solved numerically using Newton’s method. We generalize the method to any ω-continuous semiring and show that it converges faster to the least fixed point than the Kleene sequence 0, F (0), F (F (0)), . . . ...

In some recent works, a general framework for nite domains constraint satisfaction has been deened, where classical CSPs, fuzzy CSPs, weighted CSPs, partial CSPs and others can be easily cast. This framework, based on a semiring structure, allows, under certain conditions , to compute arc-consistency. Restricting to that case and integrating semiring-based constraint solving in the Constraint L...

In recent years, soft sets have become popular in various fields. For this reason, many studies been carried out the field of algebra. study, intersection k-ideals are defined with help a semiring, and some algebraic structures examined. Moreover, quotient rings by k-semiring. Isomorphism theorems examined rings. Finally, properties investigated defining maximal k-ideals.

Assumed that (S,+,.) is a semiring. Semiring algebra structure as generalization of ring. A set I⊆S called an ideal over semiring S if for any α,β∈I, we have α-β∈I and sα=αs∈I every s in S. Based on this definition, there special condition namely prime P, when αβ∈P, then could prove α or β are elements P. Furthermore, I irreducible Ia intersection from B S, I=A I=B. We also know the strongly no...

Aiming for a systematic feature extraction from time series, we introduce the iterated-sums signature over arbitrary commutative semirings. The case of tropical semiring is central, and our motivating, example. It leads to features (real-valued) series that are not easily available using existing signature-type objects. We demonstrate how extracts chronological aspects its calculation possible ...

A Kleene algebra (K,+, ·,∗ , 0, 1) is an idempotent semiring with an iteration ∗ as axiomatised by Kozen. We consider left semiring modules (A,+, 0, :) over Kleene algebras. We call such a left semiring module a Kleene module if each linear equation x = a + r : x has a least solution, where : is the product from K × A to A. The linear context-free languages can be viewed as a Kleene module A ov...