(m,n)-Semirings and a Generalized Fault Tolerance Algebra of Systems
General Mathematics
2013-04-25 v3
Abstract
We propose a new class of mathematical structures called (m,n)-semirings} (which generalize the usual semirings), and describe their basic properties. We also define partial ordering, and generalize the concepts of congruence, homomorphism, ideals, etc., for (m,n)-semirings. Following earlier work by Rao, we consider a system as made up of several components whose failures may cause it to fail, and represent the set of systems algebraically as an (m,n)-semiring. Based on the characteristics of these components we present a formalism to compare the fault tolerance behaviour of two systems using our framework of a partially ordered (m,n)-semiring.
Keywords
Cite
@article{arxiv.1005.4996,
title = {(m,n)-Semirings and a Generalized Fault Tolerance Algebra of Systems},
author = {Syed Eqbal Alam and Shrisha Rao and Bijan Davvaz},
journal= {arXiv preprint arXiv:1005.4996},
year = {2013}
}
Comments
26 pages; extension of arXiv:0907.3194v1 [math.GM]