Automata column

Abstract

In this automata column, Jöel Ouaknine and James Worrell beautifully write about beautiful recent work on linear recurrence sequences, which are sequences of integers defined by recursion like in the Fibonacci sequence. Clearly such sequences can appear almost everywhere, so there is no particularly good reason to talk about them in the automata column, but the authors politely point out such sequences can be used to count the number of words of given length accepted by an automaton. Thanks to this connection we get to have an automata column that cites Terrence Tao and uses logarithms of algebraic numbers.