Associative closure and periodicity of ω-words

摘要

We investigate some shuffle-like operations on ω-words and ω-languages. The operations are introduced using a uniform method based on the notion of an ω-trajectory. Our main results concern associativity. An interconnection between associative closure and periodicity will be exhibited. This provides characterizations of periodic and ultimately periodic ω-words. Finally, a remarkable property of the Fibonacci ω-word is proved, i.e., the associative closure of this ω-word properly contains all periodic ω-words.