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The Tribonacci constant and finite automata (2510.10834v1)
Published 12 Oct 2025 in cs.FL, cs.DM, and math.NT
Abstract: We show that there is no automaton accepting the Tribonacci representations of $n$ and $x$ in parallel, where $\psi = 1.839\cdots$ is the Tribonacci constant, and $x= \lfloor n \psi \rfloor$. Similarly, there is no Tribonacci automaton generating the Sturmian characteristic word with slope $\psi-1$.
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