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

Syed Eqbal Alam; Shrisha Rao; Bijan Davvaz

doi:10.1155/2013/482391

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arXiv · 1005.4996

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

Syed Eqbal Alam·Shrisha Rao·Bijan Davvaz

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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.

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BibTeX RIS

Syed Eqbal Alam, Shrisha Rao, Bijan Davvaz. 2013-02-07. (m,n)-Semirings and a Generalized Fault Tolerance Algebra of Systems. https://doi.org/10.1155/2013%2F482391

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