Acta Informatica

, 46:533

On regular tree languages and deterministic pushdown automata

Original Article

DOI: 10.1007/s00236-009-0104-9

Cite this article as:
Janoušek, J. & Melichar, B. Acta Informatica (2009) 46: 533. doi:10.1007/s00236-009-0104-9

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.

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of Computer Science, Faculty of Information TechnologiesCzech Technical University in PraguePraha 6Czech Republic
  2. 2.Department of Computer Science and Engineering, Faculty of Electrical EngineeringCzech Technical University in PraguePrague 2Czech Republic