Theory of Computing Systems

, Volume 54, Issue 1, pp 111–148 | Cite as

Word-Mappings of Level 2

  • Julien Ferté
  • Nathalie Marin
  • Géraud Sénizergues
Article
First Online:

Abstract

A sequence of natural numbers is said to have level k, for some natural integer k, if it can be computed by a deterministic pushdown automaton of level k (Fratani and Sénizergues in Ann Pure Appl. Log. 141:363–411, 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 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.

Keywords

Iterated pushdown automata L-systems Integer sequences Rational power series Word sequences Word equations 
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Notes

Acknowledgements

This work has been partly supported by the project ANR 2010 BLAN 0202 01 FREC. We thank the referees for their helpful remarks.

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Julien Ferté
    • 1
  • Nathalie Marin
    • 2
  • Géraud Sénizergues
    • 2
  1. 1.LIFUniversité d’Aix-Marseille 1MarseilleFrance
  2. 2.LaBRIUniversité Bordeaux 1BordeauxFrance

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