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Hierarchies of principal twist-closed trios

  • Automata and Formal Language II
  • Conference paper
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STACS 98 (STACS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1373))

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Abstract

The language theoretic operation twist from [JaPe 94] is studied in connection with the semiAFLs of languages accepted by reversal bounded multipushdown and multicounter acceptors. It is proved that the least twist-closed trio generated by MIR := { rev www ⊂ {a,b}*} is equal to the family of languages accepted in quasi-realtime by nondeterministic one-way multipushdown acceptors which operate in such a way that in every computation each pushdown makes at most one reversal. Thus, M∩(MIR) = M twist (MIR) and this family is a principal twist-closed semiAFL with a linear context-free generator. This is in contrast to the semiAFL of languages accepted by reversal-bounded multicounter machines in quasi-realtime. This family is a well known semiAFL which is principal as an intersection-closed semiAFL with generator B 1 := {a n−n1 a1 | n ⊂ IN}, see [Grei 78], but is not principal as a semiAFL. It is here shown that it forms a hierarchy of twist-closed semiAFLs and therefore is not principal as twist-closed semiAFL.

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Authors and Affiliations

  1. Universität Hamburg FB Informatik, Universität Hamburg, Vogt-Kölln-Straße 30, 22527, Hamburg

    Matthias Jantzen

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  1. Matthias Jantzen
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Michel Morvan Christoph Meinel Daniel Krob

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© 1998 Springer-Verlag

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Jantzen, M. (1998). Hierarchies of principal twist-closed trios. In: Morvan, M., Meinel, C., Krob, D. (eds) STACS 98. STACS 1998. Lecture Notes in Computer Science, vol 1373. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028573

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  • DOI: https://doi.org/10.1007/BFb0028573

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64230-5

  • Online ISBN: 978-3-540-69705-3

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