We introduce the notions of Jacobson radical of a Γ−semiring and semisimple Γ−semiring and characterize them via operator semirings. AMS Mathematics Subject Classification (2000): 16Y60, 16Y99, 20N10

We prove that the endomorphism semiring of a nontrivial semilattice is always subdirectly irreducible and describe its monolith. The endomorphism semiring is congruence simple if and only if the semilattice has both a least and a largest element.

We introduce and study the notion of a completely regular ternary semiring. Necessary and sufficient conditions for a ternary semiring to be completely regular are furnished. AMS Mathematics Subject Classification (2010): 16Y30, 16Y99

In this lecture, we summarize the interprocedural-dataflow-analysis method of Esparza et al., which generalizes Newton’s method from a numerical-analysis algorithm for finding roots of real-valued functions to a method for finding fixed-points of systems of equations over semirings. As in its real-valued counterpart, each iteration of the method of Esparza et al. solves a simpler “linearized” p...

In 1996 Zhou and Hansen proposed a first-order interval logic called Neighbourhood Logic (NL) for specifying liveness and fairness of computing systems and also defining notions of real analysis in terms of expanding modalities. After that, Roy and Zhou presented a sound and relatively complete Duration Calculus as an extension of NL. We present an embedding of NL into an idempotent semiring of...

In this paper, we made an attempt to study the algebraic nature of antifuzzy subsemiring of a semiring and we introduce the some theorems in anti-fuzzy subsemiring of a semiring. 2000 AMS Subject classification: 03F55, 06D72, 08A72.

Message passing over a factor graph can be considered as a generalization of the many well-known algorithms for an efficient marginalization of multivariate functions. The specific instance of the algorithm is obtained by selection of an appropriate commutative semiring for the range of the function to be marginalized. Some of the examples are the Viterbi algorithm, obtained on a max-product se...

The variety of power domain constructions proposed in the literature is put into a general algebraic framework. Power constructions are considered algebras on a higher level: for every ground domain, there is a power domain whose algebraic structure is speciied by means of axioms concerning the algebraic properties of the basic operations empty set, union, singleton, and extension of functions....