This paper explores lexicographic semirings and their application to problems in speech and language processing. Specifically, we present two instantiations of binary lexicographic semirings, one involving a pair of tropical weights, and the other a tropical weight paired with a novel string semiring we term the categorial semiring. The first of these is used to yield an exact encoding of backo...

The purpose of this paper is to study semirings and its ideals by neutrosophic soft sets. After noting some preliminary ideas for subsequent use in Section 1 and 2, I have introduced and studied neutrosophic soft semiring, neutrosophic soft ideals, idealistic neutrosophic soft semiring, regular (intra-regular) neutrosophic soft semiring along with some of their characterizations in Section 3 an...

The asymmetric cipher protocol, based on decomposition problem in matrix semiring M over semiring of natural numbers N is presented. The security of presented cipher protocol is based on matrix decomposition problem (MDP), which is linked to the problem of solution of multivariate polynomial system of equations. Compromitation of proposed scheme relies on the solution of system of multivariate ...

We extend an earlier algebraic approach to Neighbourhood Logic (NL) from domain semirings to lazy semirings yielding lazy semiring neighbours. Furthermore we show three important applications for these. The first one extends NL to intervals with infinite length. The second one applies lazy semiring neighbours in an algebraic semantics of the branching time temporal logic CTL∗. The third one set...

In this paper we study the notion of Smarandache semirings and semifields and obtain some interesting results about them. We show that not every semiring is a Smarandache semiring. We similarly prove that not every semifield is a Smarandache semifield. We give several examples to make the concept lucid. Further, we propose an open problem about the existence of Smarandache semiring S of finite ...

We study the free objects in variety of semigroups and monoids generated by monoid all n×n upper triangular matrices over a commutative semiring. obtain explicit representations these, as multiplicative subsemigroups quiver algebras polynomial semirings. A case particular interest is where n=2 semiring tropical semifield, coincides with that bicyclic (or equivalently, monogenic inverse monoid);...