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On regular tree languages and deterministic pushdown automata

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Abstract

The theory of formal string languages and of formal tree languages are both important parts of the theory of formal languages. Regular tree languages are recognized by finite tree automata. Trees in their postfix notation can be seen as strings. This paper presents a simple transformation from any given (bottom-up) finite tree automaton recognizing a regular tree language to a deterministic pushdown automaton accepting the same tree language in postfix notation. The resulting deterministic pushdown automaton can be implemented easily by an existing parser generator because it is constructed for an LR(0) grammar, and its size directly corresponds to the size of the deterministic finite tree automaton. The class of regular tree languages in postfix notation is a proper subclass of deterministic context-free string languages. Moreover, the class of tree languages which are in their postfix notation deterministic context-free string languages is a proper superclass of the class of regular tree languages.

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Authors and Affiliations

  1. Department of Computer Science, Faculty of Information Technologies, Czech Technical University in Prague, Kolejni 550/2, 160 00, Praha 6, Czech Republic

    Jan Janoušek

  2. Department of Computer Science and Engineering, Faculty of Electrical Engineering, Czech Technical University in Prague, Karlovo nám. 13, 121 35, Prague 2, Czech Republic

    Bořivoj Melichar

Authors
  1. Jan Janoušek
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  2. Bořivoj Melichar
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Correspondence to Jan Janoušek.

Additional information

This research has been partially supported by the Czech Ministry of Education, Youth and Sports under research program MSMT 6840770014, and by the Czech Science Foundation as project No. 201/09/0807.

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Janoušek, J., Melichar, B. On regular tree languages and deterministic pushdown automata. Acta Informatica 46, 533–547 (2009). https://doi.org/10.1007/s00236-009-0104-9

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