Finite-state dimensions of CE_b(A) and CE_b(p(A)) can be independently prescribed for any s,s' in [0,1] when p is linear with real coefficients; rational linear p preserves dimension but higher-degree rational p and integer-valued monomials can reduce it, including from 1 to below 1.
Automatic Kolmogorov complexity, normality, and finite-state dimension revisited
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Finite-State Dimension and The Davenport Erd\H{o}s Theorem
Finite-state dimensions of CE_b(A) and CE_b(p(A)) can be independently prescribed for any s,s' in [0,1] when p is linear with real coefficients; rational linear p preserves dimension but higher-degree rational p and integer-valued monomials can reduce it, including from 1 to below 1.