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Antonin Delpeuch (Oct 02 2020 at 19:48):An axiomatization of finite state automata with string diagrams by @Robin Piedeleu and Fabio Zanasi. I find this very exciting, check it out! https://arxiv.org/abs/2009.14576
Cole Comfort (Oct 02 2020 at 21:42):Wow these string diagrams look pretty cool! It is nice that people are giving finite presentations of strict symmetric monioidal categories which aren't just props.
Robin Piedeleu (Oct 03 2020 at 10:33):Thanks, Antonin! Of course, I'm happy to answer questions about it here if you have any.
Robin Piedeleu (Oct 03 2020 at 10:36):We're still working on polishing it for submission and eliminating typos etc. (for example, at the moment, Brzozowski's algorithm is the wrong way around. But this has no incidence on the proof, luckily). So we're happy to receive feedback if you have any!
Robin Piedeleu (Oct 03 2020 at 10:40):I am also still a bit unsatisfied with the trick of adding the red wires to reintroduce regexes into the syntax. Our original goal was to kill the Kleene star so we have not fully succeeded yet! But this is only one side of the story: there is richer structure in this category that we're hoping to exploit to fully eliminate the star from the syntax. This is ongoing work...