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math.NT2017
A density version of Cobham's theorem
Jakub Byszewski, Jakub Konieczny
Cobham's theorem asserts that if a sequence is automatic with respect to two multiplicatively independent bases, then it is ultimately periodic. We prove a stronger density version…
math.NT2017★ 5 cited
Automatic sequences and generalised polynomials
Jakub Byszewski, Jakub Konieczny
We conjecture that bounded generalised polynomial functions cannot be generated by finite automata, except for the trivial case when they are ultimately periodic. Using methods fro…