State Complexity of Combined Operations for Prefix-Free Regular Languages

Abstract

We investigate the state complexity of combined operations for prefix-free regular languages. Prefix-free minimal deterministic finite-state automata have a unique structural property that plays an important role to obtain the precise state complexity of basic operations. Based on the same property, we establish the precise state complexity of four combined operations: star-of-union. star-of-intersection, star-of-reversal and star-of-catenation.