May I know the developments in pure algebra and automata theory ?

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Dennis P. Allen Jr.

Yes, just follow Prof. Emeritus John Rhodes on ResearchGate as he is the expert in automata and their algebraic properties.

Yuri S Semenov

Maybe https://en.wikipedia.org/wiki/Automatic_group

William R. Buckley

May I suggest that my papers on Computational Ontogeny are well worth considering, when looking for the breadth of application of automata theory.