Subtree matching by pushdown automata

Abstract

Subtree matching is an important problem in Computer Science on which a number of tasks, such as mechanical theorem proving, term-rewriting, symbolic computation and nonprocedural programming languages are based on. A systematic approach to the construction of subtree pattern matchers by deterministic pushdown automata, which read subject trees in prefix and postfix notation, is presented. The method is analogous to the construction of string pattern matchers: for a given pattern, a nondeterministic pushdown automaton is created and is then determinised. In addition, it is shown that the size of the resulting deterministic pushdown automata directly corresponds to the size of the existing string pattern matchers based on finite automata.

Arbology: Trees and Pushdown Automata

“…Given an input tree t with n nodes, the searching phase of the deterministic subtree matching automaton constructed by Algorithms 2 and 1 is O(n), which is also proved in [12]. Example 6.2.…”

“…The correctness of Algorithm 2 is proved in [12]. For constructing deterministic subtree matching PDA, we use the transformation described by Algorithm 1.…”

“…For constructing deterministic subtree matching PDA, we use the transformation described by Algorithm 1. In [12] it is proved that given a tree t with n nodes in its prefix or postfix notation, the deterministic subtree matching PDA M pds (t) constructed by Algorithm 2 and 1 is made of exactly n+1 states, one pushdown symbol and |A|(n+1) transitions.…”

“…There are two matching actions in this sequence, which means there are two occurrences of subtree p 1 in tree t 3 at the corresponding positions. pref(t 3 ) = a2a2a0a1a0a2a0a1a0 Subtree matching for multiple subtrees can easily be performed by a PDA created as a union of subtree matching PDAs for the particular subtrees, for more details see [12].…”

Simple tree pattern matching for trees in the prefix bar notation

“…Based on this fundamental result, Melichar et al started to extend principles of text pattern matching using finite automata into the tree pattern matching domain. They use pushdown automata for matching in trees, where trees are represented by their prefix or postfix notation [13,9,10]. These automata are either constructed directly as deterministic pushdown automata, or they are nondeterministic visual pushdown automata.…”