Quotient Complexity of Ideal Languages

We study the state complexity of regular operations in the class of ideal languages. A language L ⊆ Σ∗ is a right (left) ideal if it satisfies L = LΣ∗ (L = Σ∗L). It is a two-sided ideal if L = Σ∗LΣ∗, and an all-sided ideal if L = Σ∗ L, the shuffle of Σ∗ with L. We prefer the term “quotient complexity” instead of “state complexity”, and we use derivatives to… CONTINUE READING