TL;DR
This paper develops an algebraic framework to analyze fault tolerance in complex systems by modeling their composition using monoids and semirings, enabling systematic comparison of fault-tolerance properties.
Contribution
It introduces an algebraic structure for fault tolerance analysis based on system composition, providing a formal method to compare and reason about fault-tolerance.
Findings
Systems form monoids under composition operators
A semiring structure is established for combined compositions
Partial orderings enable fault-tolerance comparisons
Abstract
Every system of any significant size is created by composition from smaller sub-systems or components. It is thus fruitful to analyze the fault-tolerance of a system as a function of its composition. In this paper, two basic types of system composition are described, and an algebra to describe fault tolerance of composed systems is derived. The set of systems forms monoids under the two composition operators, and a semiring when both are concerned. A partial ordering relation between systems is used to compare their fault-tolerance behaviors.
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Taxonomy
TopicsDistributed systems and fault tolerance · Logic, programming, and type systems · Petri Nets in System Modeling