Thermodynamic semirings are deformed additive structures on characteristic one semirings, defined using a binary information measure. The algebraic properties of the semiring encode thermodynamical and information theoretic properties of the entropy function. Besides the case of the Shannon entropy, which arises in the context of geometry over the field with one element and the Witt constructio...

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...

A Conway semiring is a semiring S equipped with a unary operation * : S → S, always called 'star', satisfying the sum star and product star identities. It is known that these identities imply a Kleene type theorem. Some computationally important semirings, such as N or N rat Σ * of rational power series of words on Σ with coefficients in N, cannot have a total star operation satisfying the Conw...

Digital signatures are probably the most important and widely used cryptographic primitive enabled by public key technology, and they are building blocks of many modern distributed computer applications, like, electronic contract signing, certified email, and secure web browsing etc. But many existing signatures schemes lie in the intractability of problems closely related to the number theory ...

In this paper, we propose a new signature scheme connecting two private keys and two public keys based on general non-commutative division semiring. The key idea of our technique engrosses three core steps. In the first step, we assemble polynomials on additive structure of non-commutative division semiring and take them as underlying work infrastructure. In the second step, we generate first s...

This paper is a survey on universal algorithms for solving the matrix Bellman equations over semirings and especially tropical and idempotent semirings. However, original algorithms are also presented. Some applications and software implementations are discussed.

|We introduce the notions of fuzzy ternary subsemiring, fuzzy ideal and quasi-ideal in ternary semirings and study some properties of these two ideals. We also study the properties of fuzzy ideal and fuzzy quasi-ideal of ternary semirings.

In this paper we describe a computer program for searching all four-element multiplicatively idempotent semirings. We have established that up to the isomorphism of such semirings exactly 381, they are represented by Cayley tables additive and multiplicative reducts. give necessary definitions, properties illustrations.