Automatic multiplicative sequences

Abstract: Automatic sequences $-$ that is, sequences computable by finite automata $-$ give rise to one of the most basic models of computation. As such, for any class of sequences it is natural to ask which sequences in it are automatic. In particular, the question of classifying automatic multiplicative sequences has attracted considerable attention in the recent years. In the completely multiplicative case, such classification was obtained independently by S. Li and O. Klurman and P. Kurlberg. The main topic of my talk will be the resolution of the general case, obtained in a recent preprint with Lemańczyk and C. Müllner. I will also discuss some early results on classification of automatic semigroups, which is the subject of ongoing work with O. Klurman.

number theory

Audience: researchers in the topic

Combinatorial and additive number theory (CANT 2021)

Series comments: This is the nineteenth in a series of annual workshops sponsored by the New York Number Theory Seminar on problems in combinatorial and additive number theory and related parts of mathematics.

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