The operad of temporal wiring diagrams: formalizing a graphical language for discrete-time processes

Understand

We investigate the hierarchical structure of processes using the mathematical theory of operads.

• Information or material enters a given process as a stream of inputs, and the process converts it to a stream of outputs.
• Output streams can then be supplied to other processes in an organized manner, and the resulting system of interconnected processes can itself be considered a macro process.
• To model the inherent structure in this kind of system, we define an operad $\mathcal{W}$ of black boxes and directed wiring diagrams, and we define a $\mathcal{W}$-algebra $\mathcal{P}$ of processes (which we call propagators, after Radul and Sussman).