(m, n)-Semirings and a Generalized Fault Tolerance Algebra of Systems
Syed Eqbal Alam
Broschiertes Buch

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

Generalization of fault tolerance algebra of systems

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We propose a new class of mathematical structures called (m, n)-semirings (which generalize the usual semirings), and describe their basic properties. We also de ne partial ordering, and generalize the concepts of congruence, homomorphism, etc., for (m, n)-semirings. Following earlier work by Rao [37], 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 behavior of two systems using ou...