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On Bounded Languages and Reversal-Bounded Automata

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7810)

Abstract

Bounded context-free languages have been investigated for nearly fifty years, yet they continue to generate interest as seen from recent studies. Here, we present a number of results about bounded context-free languages. First we give a new (simpler) proof that every context-free language \(L \subseteq w_1^* w_2^* ... w_n^*\) can be accepted by a PDA with at most 2n − 3 reversals. We also introduce new collections of bounded context-free languages and present some of their interesting properties. Some of the properties are counter-intuitive and may point to some deeper facts about bounded CFL’s. We present some results about semilinear sets and also present a generalization of the well-known result that over a one-letter alphabet, the family of context-free and regular languages coincide.

Keywords

  • context-free language (CFL)
  • nondeterministic pushdown automaton (NPDA)
  • reversal-bounded
  • semilinear set
  • stratified linear set

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Ibarra, O.H., Ravikumar, B. (2013). On Bounded Languages and Reversal-Bounded Automata. In: Dediu, AH., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2013. Lecture Notes in Computer Science, vol 7810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37064-9_32

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  • DOI: https://doi.org/10.1007/978-3-642-37064-9_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37063-2

  • Online ISBN: 978-3-642-37064-9

  • eBook Packages: Computer ScienceComputer Science (R0)