Word-Mappings of level 3

01/24/2023

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by   G. Sénizergues, et al.

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Sequences of numbers (either natural integers, or integers or rational) of level k ∈ℕ have been defined in <cit.> as the sequences which can be computed by deterministic pushdown automata of level k. This definition has been extended to sequences of words indexed by words in <cit.>. We characterise here the sequences of level 3 as the compositions of two HDT0L-systems. Two applications are derived: - the sequences of rational numbers of level 3 are characterised by polynomial recurrences - the equality problem for sequences of rational numbers of level 3 is decidable.