[Berkeley Seminar] Keri D'Angelo: Composing Instantaneous Machines

Title: Composing Instantaneous Machines
Abstract: In this talk, I’ll discuss recent progress Sophie and I have made on composing instantaneous machines. Instantaneous machines means that at any point in time, input can be given to the machine and the machine will give output based on this input and its current state. In this talk, I’ll show how we can compose such machines. We first create an extended category of directed wiring diagrams accounting for the dependency between input and output, and then define an operad algebra giving us the semantics that defines composition. Depending on where the interest lies, we can delve into some details including that since the output now depends on the input, we come into the “problem” that every time the output changes, the input may also change. This can be accounted for by giving a fixed point that shows after finite time, our input and output will stabilize.
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