3 problems

Fibonacci nonautomaticity conjecture. The sequence $d_f$ of the Fibonacci word $\mathbf{u}_f$ is not Fibonacci-automatic, and consequently the prefix palindromic length…

Period-doubling nonautomaticity conjecture. The sequence $d_{pd}$ of the period-doubling word $\mathbf{u}_{pd}$ is not $2$-automatic, and consequently the prefix palindromic length…

PPL-difference automaticity conjecture. The PPL-difference sequence $d_{\mathbf{u}}$ of a $k$-automatic word is always $k$-automatic.