arXiv 2103.095872021-03cs.FL

Regularity Conditions for Iterated Shuffle on Commutative Regular Languages

Stefan Hoffmann

备注：: Accepted at CIAA 2021. Incorporated the remarks by the referees

英文摘要：

We identify a subclass of the regular commutative languages that is closed under the iterated shuffle, or shuffle closure. In particular, it is regularity-preserving on this subclass. This subclass contains the commutative group languages and, for every alphabet $Σ$, the class $\textbf{Com}^+(Σ^*)$ given by the ordered variety $\textbf{Com}^+$. Then, we state a simple characterization when the iterated shuffle on finite commutative languages gives a regular language again and state partial results for aperiodic commutative languages. We also show that the aperiodic, or star-free, commutative languages and the commutative group languages are closed under projection.

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