On Tree Pattern Matching by Pushdown Automata

T. Flouri

doi:10.14311/1113

Abstract

Tree pattern matching is an important operation in Computer Science on which a number of tasks such as mechanical theorem proving, term-rewriting, symbolic computation and non-procedural programming languages are based on. Work has begun on a systematic approach to the construction of tree pattern matchers by deterministic pushdown automata which read subject trees in prefix notation. The method is analogous to the construction of string pattern matchers: for given patterns, a non-deterministic pushdown automaton is created and then it is determinised. In this first paper, we present the proposed non-deterministic pushdown automaton which will serve as a basis for the determinisation process, and prove its correctness.

Highlights

Tree pattern matching is one of the fundamental problems with many applications, and is often declared to be analogous to the problem of string pattern matching [3, 5, 17]
One of the basic approaches used for string pattern matching is represented by finite automata which are constructed for string patterns, which means that the patterns are preprocessed
This paper presents the first attempt to perform tree pattern matching by a unified and systematic approach using pushdown automata

Summary

Introduction

Tree pattern matching is one of the fundamental problems with many applications, and is often declared to be analogous to the problem of string pattern matching [3, 5, 17]. String pattern matching is the problem of finding all occurrences of string patterns and their positions in a given text. Given a text of size n, such finite automata typically perform the search phase in time linear to n (see [8, 9, 19] for a survey). Basic, non-deterministic model of a pushdown automaton performing tree pattern matching. The goal of this research is to provide a method for determinising the non-deterministic model of the proposed pushdown automaton, which will make linear time (based on the size of the subject tree) pattern matching possible

Basic notions

A Deterministic Pushdown Automaton accepting trees in prefix notation

Searching Non-Deterministic Pushdown Automaton

Conclusion and future work