(m,n)-Semirings and a Generalized Fault Tolerance Algebra of Systems
arXiv:1005.4996 · doi:10.1155/2013/482391
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.
arXiv comment26 pages; extension of arXiv:0907.3194v1 [math.GM]