Look into Antimirov Derivatives

[gallais]

Cf. https://semantic-domain.blogspot.com/2013/11/antimirov-derivatives-for-regular.html

The current algorithm does not quotient derivatives over associativity, commutativity and idempotence rules (it does however quotient over identity rules). But we can do better:

we can construct sets of partial derivatives, which collectively accept the same strings as the Brzozowski derivative. The idea is that we can use the algebraic properties of sets to model the effect of the ACUI equations