(m,n)-Semirings and a Generalized Fault Tolerance Algebra of Systems

Details (m,n)-Semirings and a Generalized Fault Tolerance Algebra of Systems (m,n)-Semirings and a Generalized Fault Tolerance Algebra of Systems

2010-05-27

arxiv.org/abs/1005.4996v2

Mathematics

General Mathematics

26 pages; extension of arXiv:0907.3194v1 [math.GM]

Scientific paper

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.

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