Word-Mappings of level $3$
Formal Languages and Automata Theory
2023-10-12 v2 Computational Complexity
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.
Cite
@article{arxiv.2301.09966,
title = {Word-Mappings of level $3$},
author = {G. Sénizergues},
journal= {arXiv preprint arXiv:2301.09966},
year = {2023}
}
Comments
46 pages. 1 figure