Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Modeling Hierarchical Systems with Operads



Spencer Breiner, Olivier Marie Rose, Blake S. Pollard, Eswaran Subrahmanian


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 rel- ative probabilities of component failure in the system. Finally, we show how to extend the analysis from general component failure to specific failure modes.
Proceedings Title
Proceedings Applied Category Theory 2019
Conference Dates
July 15-19, 2019
Conference Location
Oxford, GB


Applied Category Theory, Operad, Length Measurement System, Functorial Semantics, Hierarchical Systems


Breiner, S. , Marie Rose, O. , Pollard, B. and Subrahmanian, E. (2020), Modeling Hierarchical Systems with Operads, Proceedings Applied Category Theory 2019, Oxford, GB, [online], (Accessed April 15, 2024)
Created November 4, 2020, Updated February 16, 2024