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Regulated Nondeterminism in Pushdown Automata

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Implementation and Application of Automata (CIAA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4783))

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Abstract

A generalization of pushdown automata towards regulated nondeterminism is studied. The nondeterminism is governed in such a way that the decision, whether or not a nondeterministic rule is applied, depends on the whole content of the stack. More precisely, the content of the stack is considered as a word over the stack alphabet, and the pushdown automaton is allowed to act nondeterministically, if this word belongs to some given set R of control words. Otherwise its behavior is deterministic. The computational capacity of such R -PDAs depends on the complexity of R. It turns out that non-context-free languages are accepted even if R is a linear, deterministic context-free language. On the other hand, regular control sets R do not increase the computational capacity of nondeterministic pushdown automata. This raises the natural question for the relations between the structure and complexity of regular sets R on one hand and the computational capacity of the corresponding R -PDA on the other hand. Clearly, if R is empty, the deterministic context-free languages are characterized. For R = {a,b}* one obtains all context-free languages. Furthermore, if R is finite, then the regular closure of the deterministic context-free languages is described. We investigate these questions, and discuss closure properties of the language classes in question under AFL operations.

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Authors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392 Giessen, Germany

    Martin Kutrib & Larissa Werlein

  2. Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt, 60054 Frankfurt am Main, Germany

    Andreas Malcher

Authors
  1. Martin Kutrib
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  2. Andreas Malcher
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  3. Larissa Werlein
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Jan Holub Jan Žďárek

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© 2007 Springer-Verlag Berlin Heidelberg

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Kutrib, M., Malcher, A., Werlein, L. (2007). Regulated Nondeterminism in Pushdown Automata. In: Holub, J., Žďárek, J. (eds) Implementation and Application of Automata. CIAA 2007. Lecture Notes in Computer Science, vol 4783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76336-9_10

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  • DOI: https://doi.org/10.1007/978-3-540-76336-9_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-76335-2

  • Online ISBN: 978-3-540-76336-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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