Modeling Hierarchical System with Operads

Spencer Breiner
Blake Pollard
Eswaran Subrahmanian
Olivier Marie-Rose
(Prometheus Computing)

This paper applies operads and functorial semantics to address the problem of failure diagnosis in complex systems. We start with a concrete example, developing a hierarchical interaction model for the Length Scale Interferometer, a high-precision measurement system operated by the US National Institute of Standards and Technology. The model is expressed in terms of combinatorial/diagrammatic structures called port-graphs, and we explain how to extract an operad LSI from a collection of these diagrams. Next we show how functors to the operad of probabilities organize and constrain the relative probabilities of component failure in the system. Finally, we show how to extend the analysis from general component failure to specific failure modes.

In John Baez and Bob Coecke: Proceedings Applied Category Theory 2019 (ACT 2019), University of Oxford, UK, 15-19 July 2019, Electronic Proceedings in Theoretical Computer Science 323, pp. 72–83.
Published: 15th September 2020.

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