Duality of Lattices Associated to Left and Right Quotients

We associate lattices to the sets of unions and intersections of left and right quotients of a regular language. For both unions and intersections, we show that the lattices we produce using left and right quotients are dual to each other. We also give necessary and sufficient conditions for these lattices to have maximal possible complexity.Comment: In Proceedings AFL 2023, arXiv:2309.0112