State Complexity Investigations on Commutative Languages -- The Upward and Downward Closure, Commutative Aperiodic and Commutative Group Languages

Abstract: We investigate the state complexity of the upward and downward closure and interior operations on commutative regular languages. Then, we systematically study the state complexity of these operations and of the shuffle operation on commutative group languages and commutative aperiodic (or star-free) languages.