In examples, we'll still use juxtaposition to denote concatenation. The derivative for regular languages The useful property of the derivative from an implementation point of view is that it has a recursive definition over regular languages: Dc(∅) = ∅ Dc(ε) = ∅ Dc(c) = ε Dc(c') = ∅ if c is not c' Dc(A ○ B) = Dc(A) ○ B if A does not contain the empty string Dc(A ○ B) = Dc(A) ○ B ∪ Dc(B) if A contai