Abstract
The ordered structures of polynomial idempotent algebras over max-plus algebra are investigated in this paper. Based on the antisymmetry, the partial orders on the sets of formal polynomials and polynomial functions are introduced to generate two partially ordered idempotent algebras (POIAs). Based on the symmetry, the quotient POIA of formal polynomials is then obtained. The order structure relationships among these three POIAs are described: the POIA of polynomial functions and the POIA of formal polynomials are orderly homomorphic; the POIA of polynomial functions and the quotient POIA of formal polynomials are orderly isomorphic. By using the partial order on formal polynomials, an algebraic method is provided to determine the upper and lower bounds of an equivalence class in the quotient POIA of formal polynomials. The criterion for a formal polynomial to be the minimal element of an equivalence class is derived. Furthermore, it is proven that any equivalence class is either an uncountable set with cardinality of the continuum or a finite set with a single element.
Funder
National Natural Science Foundation of China
China Postdoctoral Science Foundation
Subject
Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)
Reference37 articles.
1. Minimax Algebra;Cuninghame-Green,1979
2. Synchronization and Linearity: An Algebra for Discrete Event System;Baccelli,1992
3. Max-Plus at Work: Modeling and Analysis of Synchronized Systems;Heidergott,2006
4. Max-Linear Systems: Theory and Algorithms;Butkovič,2010
5. A linear-system-theoretic view of discrete-event processes and its use for performance evaluation in manufacturing
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献