TL;DR
This paper characterizes level 3 word-mapped sequences as compositions of two HDT0L-systems, providing a framework for understanding their structure, and demonstrates applications including polynomial recurrence characterization and decidability of equality for rational sequences.
Contribution
It introduces a novel characterization of level 3 sequences as compositions of two HDT0L-systems, extending previous definitions to words and sequences of higher complexity.
Findings
Sequences of rational numbers of level 3 are characterized by polynomial recurrences.
The equality problem for sequences of rational numbers of level 3 is decidable.
Sequences of level 3 can be represented as compositions of two HDT0L-systems.
Abstract
Sequences of numbers (either natural integers, or integers or rational) of level have been defined in \cite{Fra05,Fra-Sen06} as the sequences which can be computed by deterministic pushdown automata of level . This definition has been extended to sequences of {\em words} indexed by {\em words} in \cite{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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Taxonomy
Topicssemigroups and automata theory · Coding theory and cryptography · Cellular Automata and Applications