Some public-key cryptosystems based on the tropical semiring have been proposed in recent years because of their increased efficiency, since multiplication is actually an ordinary addition numbers and there no semiring. However, most these security defects they adopt a public matrix to construct commutative semirings. This paper proposes new circular matrices. The relies NP-hard problem solving...

For a top semimodule over semiring with zero and nonzero identity, this paper studies the interplay between topological properties of subtractive prime spectrum algebraic semimodule. We prove that subtractively finitely generated is compact space, establish necessary sufficient conditions for to be generated. For
 multiplication commutative semiring, we radical subsemimodule coincides its ...

Pushdown systems (PDSs) and recursive state machines (RSMs), which are linearly equivalent, are standard models for interprocedural analysis. Yet RSMs are more convenient as they (a) explicitly model function calls and returns, and (b) specify many natural parameters for algorithmic analysis, e.g., the number of entries and exits. We consider a general framework where RSM transitions are labele...

Cost functions for tree automata are mappings from transitions to (tuples o0 polynomials over some semiring. We consider four semirings, namely N the semiring of nonnegative integers, A the "arctical semiring", T the tropical semiring and F the semiring of finite subsets of nonnegative integers. We show: for semirings N and A it is decidable in polynomial time whether or not the costs of accept...

The interplay between topological hyperconvex spaces and sigma-finite measures in such gives rise to a set of analytical observations. This paper introduces the Noetherian class k-finite k-hyperconvex subspaces (NHCs) admitting countable finite covers. A measure is constructed sigma-semiring NHC under ordering NHCs. relation maintains irreflexive anti-symmetric algebraic properties while retain...

A modernization of signature scheme published in (Sakalauskas, 2004) is presented. This scheme differs from the prototype by its structure and uses a more general algebraic systems. It has a higher security and shorter key length and is also more computationally effective. The introduced new algebraic structures, semiring and semimodule, are mutually compatible algebraic systems. The semiring i...

Good and Hughes [9] introduced the notion of bi-ideal and Steinfeld [11, 12] introduced the notion of quasi-ideal. Sioson [10] studied some properties of quasi-ideals of ternary semigroups. In [1], Dixit and Dewan studied about the quasi-ideals and bi-ideals of ternary semigroups. Quasi-ideals are generalization of right ideals, lateral ideals, and left ideals whereas bi-ideals are generalizati...