Word-Mappings of level 3
Abstract
Sequences of numbers (either natural integers, or integers or rational) of level k ∈ N have been defined in Fra05,Fra-Sen06 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 Sen07,Fer-Mar-Sen14. 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.
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