@article{Brzozowski2016MostCR,
title={Most Complex Regular Ideal Languages},
author={Janusz A. Brzozowski and Sylvie Davies and Bo Yang Victor Liu},
journal={Discrete Mathematics & Theoretical Computer Science},
year={2016},
volume={18}
}

A right ideal (left ideal, two-sided ideal) is a non-empty language L over an alphabet Σ that satisfies L = LΣ∗ (L = Σ∗L, L = Σ∗LΣ∗). Let k = 3 for right ideals, 4 for left ideals and 5 for two-sided ideals. We show that there exist sequences (Ln | n > k) of right, left, and two-sided regular ideals, where Ln has quotient complexity (state complexity) n, such that Ln is most complex in its class under the following measures of complexity: the size of the syntactic semigroup, the quotient… CONTINUE READING