# Word-mappings of level 2

Abstract : A sequence of natural numbers is said to have {\em level k}, for some natural integer $k$, if it can be computed by a deterministic pushdown automaton of level $k$ ([Fratani-Sénizergues, APAL, 2006]). We show here that the sequences of level 2 are exactly the rational formal power series over one undeterminate. More generally, we study mappings {\em from words to words} and show that the following classes coincide:\\ - the mappings which are computable by deterministic pushdown automata of level $2$\\ - the mappings which are solution of a system of catenative recurrence equations\\ - the mappings which are definable as a Lindenmayer system of type HDT0L.\\ We illustrate the usefulness of this characterization by proving three statements about formal power series, rational sets of homomorphisms and equations in words.
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Journal articles

https://hal.archives-ouvertes.fr/hal-00948896
Contributor : Géraud Sénizergues <>
Submitted on : Tuesday, February 18, 2014 - 5:01:48 PM
Last modification on : Tuesday, April 2, 2019 - 1:45:35 AM

### Identifiers

• HAL Id : hal-00948896, version 1

### Citation

Julien Ferté, Nathalie Marin, Géraud Sénizergues. Word-mappings of level 2. Theory of Computing Systems, Springer Verlag, 2013, 54, pp.111-148. ⟨hal-00948896⟩

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