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arXiv · 2111.13523

Commutative Regular Languages with Product-Form Minimal Automata

Stefan Hoffmann
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Abstract

We introduce a subclass of the commutative regular languages that is characterized by the property that the state set of the minimal deterministic automaton can be written as a certain Cartesian product. This class behaves much better with respect to the state complexity of the shuffle, for which we find the bound~$2nm$ if the input languages have state complexities $n$ and $m$, and the upward and downward closure and interior operations, for which we find the bound~$n$. In general, only the bounds $(2nm)^{|\Sigma|}$ and $n^{|\Sigma|}$ are known for these operations in the commutative case. We prove different characterizations of this class and present results to construct languages from this class. Lastly, in a slightly more general setting of partial commutativity, we introduce other, related, language classes and investigate the relations between them.

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Stefan Hoffmann. 2021-11-26. Commutative Regular Languages with Product-Form Minimal Automata. https://arxiv.org/abs/2111.13523

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