SetReplace VS BernDirac

Some of the ideas in this post might pan out, some might not. Regardless, I do think token event graphs will turn out to be important. Of course, I'm biased: I coined the name TEG -- although the underlying idea originated with Max Piskunov and his "local multiway systems" [0]

What's promising about TEGs (and their incidence hypergraph, the rewrite hypergraph) is that they offer a clean methodology to decompose the behavior of a non-deterministic automaton into its causally independent parts. We're still trying to understand how to think about them, but the most promising approach seems to use the lens of (modular) representation theory, which gives us a rich mathematical toolkit to work with.

If this methodology works, there will be possibility to represent many kinds of systems in disparate fields, ranging from distributed computation to physics to biology to machine learning, in the common language of TEGs and their representations. Of course it may turn out to be merely a recasting of older ideas. In particular the Khrone-Rhodes theorem [1], categorical Petri nets [2], and the GNS construction [3] seem like they might be describing the same or an analogous procedure.

I hope to soon be describing this approach in full detail using quiver geometry [4].

[0]: https://github.com/maxitg/SetReplace/blob/master/Research/Lo...

[1]: https://www.wikiwand.com/en/Krohn–Rhodes_theory

[2]: https://arxiv.org/abs/2101.04238

[3]: https://www.youtube.com/watch?v=OmaSAG4J6nw

[4]: https://quivergeometry.net