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Context-Free Sequences

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Theoretical Aspects of Computing – ICTAC 2014 (ICTAC 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8687))

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Abstract

A sequence w over a finite alphabet A is generated by a uniform automaton if there exists an automaton labelled on {0,…,k − 1} for some k > 1 and recognizing for each output a in A the set of positions of a in w expressed in base k. Automatic sequences are generated by finite automata. By considering pushdown automata instead of finite ones, we generate exactly the context-free sequences. We distinguish the sub-families of unambiguous, deterministic, real-time deterministic context-free sequences associated with the corresponding families of pushdown automata. We study the closure under shift, product, morphisms, inverse substitutions and various extractions of these four families of context-free sequences. Additionally, we show that only using multiplicatively dependent bases yields the same set of context-free sequences.

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Author information

Authors and Affiliations

  1. CNRS, LIGM-Université Paris-Est, France

    Didier Caucal

  2. LIM, Université de la Réunion, France

    Marion Le Gonidec

Authors
  1. Didier Caucal
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  2. Marion Le Gonidec
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Editor information

Editors and Affiliations

  1. Institute of Computer Science, Romanian Academy, Blvd. King Carol I no.8, 700505, Iaşi, Romania

    Gabriel Ciobanu

  2. LORIA, Université de Lorraine, Campus Scientifique, BP 239, 54506, Vandœvre-lès-Nancy, France

    Dominique Méry

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© 2014 Springer International Publishing Switzerland

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Caucal, D., Le Gonidec, M. (2014). Context-Free Sequences. In: Ciobanu, G., Méry, D. (eds) Theoretical Aspects of Computing – ICTAC 2014. ICTAC 2014. Lecture Notes in Computer Science, vol 8687. Springer, Cham. https://doi.org/10.1007/978-3-319-10882-7_16

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  • DOI: https://doi.org/10.1007/978-3-319-10882-7_16

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10881-0

  • Online ISBN: 978-3-319-10882-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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