On regular tree languages and deterministic pushdown automata

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 g...

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Bibliographic Details
Published in:Acta informatica Vol. 46; no. 7; pp. 533 - 547
Main Authors: Janoušek, Jan, Melichar, Bořivoj
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.11.2009
Springer
Springer Nature B.V
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Analysis
Applied sciences
Automation
Combinatorics
Combinatorics. Ordered structures
Computer engineering
Computer Science
Computer science; control theory; systems
Computer Systems Organization and Communication Networks
Data Structures and Information Theory
Decision trees
Exact sciences and technology
Generators
Grammar
Graph theory
Information Systems and Communication Service
Language
Language theory and syntactical analysis
Logics and Meanings of Programs
Mathematics
Miscellaneous
Original Article
Programming languages
Sciences and techniques of general use
Software Engineering/Programming and Operating Systems
Studies
Theoretical computing
Theory of Computation
Transition rules
Trees
Ground Term
Tree Language
Tree Automaton
Transition Rule
Grammar Rule
Formal language
Language theory
Computer theory
Context free language
Deterministic automaton
Finite automaton
Regular language
Tree automaton
Implementation
Parser
Language class
Tree
Push down automaton
LR grammar
Generator
Deterministic language
ISSN:0001-5903, 1432-0525
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Summary: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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ISSN:0001-5903
1432-0525
DOI:10.1007/s00236-009-0104-9