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Sequences of Level 1, 2, 3,..., k,...

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Computer Science – Theory and Applications (CSR 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4649))

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Abstract

Sequences of numbers (either natural integers, or integers or rational) of level have been defined in [FS06] as the sequences which can be computed by deterministic pushdown automata of level k. We extend this definition to sequences of words indexed by words. We give characterisations of these sequences in terms of “higher-order” L-systems. In particular sequences of rational numbers of level 3 are characterised by polynomial recurrences (which generalize the P-recurrent sequences studied in [Sta80]). The equality problem for sequences of rational numbers of level 3 is shown decidable.

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Authors and Affiliations

  1. LaBRI and UFR Math-info, Université Bordeaux1 351 Cours de la libération -33405- Talence Cedex,  

    Géraud Sénizergues

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  1. Géraud Sénizergues
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Volker Diekert Mikhail V. Volkov Andrei Voronkov

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Sénizergues, G. (2007). Sequences of Level 1, 2, 3,..., k,.... In: Diekert, V., Volkov, M.V., Voronkov, A. (eds) Computer Science – Theory and Applications. CSR 2007. Lecture Notes in Computer Science, vol 4649. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74510-5_6

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  • DOI: https://doi.org/10.1007/978-3-540-74510-5_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74509-9

  • Online ISBN: 978-3-540-74510-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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