A Class of Automatic Sequences
Michel Rigo, Robert Underwood

TL;DR
This paper proves that the characteristic sequences of regular languages over a k-letter alphabet are k-automatic, extending to multiplicatively dependent alphabet sizes, thus linking regular languages and automatic sequences.
Contribution
It establishes a new connection between regular languages and automatic sequences for different alphabet sizes, including multiplicatively dependent cases.
Findings
Characteristic sequence of a regular language over a k-letter alphabet is k-automatic.
Extension to t-letter alphabets where t and k are multiplicatively dependent.
Provides a broader understanding of automaticity in regular languages.
Abstract
Let . We prove that the characteristic sequence of a regular language over a -letter alphabet is -automatic. More generally, if and are multiplicatively dependent, we show that the characteristic sequence of a regular language over a -letter alphabet is -automatic.
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Taxonomy
Topicssemigroups and automata theory · Algorithms and Data Compression · DNA and Biological Computing
