Tropical semiring has proven successful in several research areas, including optimal control, bioinformatics, discrete event systems, or solving a decision problem. In previous studies, matrix two-factorization algorithm based on the tropical been applied to investigate bipartite and tripartite networks. Tri-factorization algorithms standard linear algebra are used for tasks such as data fusion...

We study the connections between rational series with coeecients in a semiring and their languages.

An approach to schedule development in project management is proposed based on models and methods of idempotent algebra. The approach offers a way to represent various types of precedence relationships among activities in projects as linear vector equations in terms of an idempotent semiring. As a result, many issues in project scheduling reduce to solving computational problems in the idempote...

On the space of nondepraved (see [8]) real, isolated singularities, we consider the stable equivalence relation induced by smooth deformations whose asymptotic behaviour is controlled by the Palais-Smale condition. It is shown that the resulting space of equivalence classes admits a canonical semiring structure and is isomorphic to the semiring of stable homotopy classes of CW-complexes. In an ...