scholarly journals On Tree Pattern Matching by Pushdown Automata

10.14311/1113 ◽  
2009 ◽  
Vol 49 (2) ◽  
Author(s):  
T. Flouri
Keyword(s):  
Programming Languages ◽  
Pattern Matching ◽  
Systematic Approach ◽  
Term Rewriting ◽  
Pushdown Automaton ◽  
Tree Pattern ◽  
Tree Pattern Matching ◽  
String Pattern ◽  
Pushdown Automata ◽  
Mechanical Theorem

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. 

scholarly journals Subtree matching by pushdown automata

2010 ◽  
Vol 7 (2) ◽  
pp. 331-357 ◽  
Author(s):  
Tomás Flouri ◽  
Jan Janousek ◽  
Bořivoj Melichar
Keyword(s):  
Programming Languages ◽  
Theorem Proving ◽  
Systematic Approach ◽  
Finite Automata ◽  
Term Rewriting ◽  
Mechanical Theorem Proving ◽  
Pushdown Automaton ◽  
String Pattern ◽  
Pushdown Automata ◽  
Mechanical Theorem

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.

scholarly journals Indexing ordered trees for (nonlinear) tree pattern matching by pushdown automata

2012 ◽  
Vol 9 (3) ◽  
pp. 1125-1153
Author(s):  
J. Travnícek ◽  
J. Janousek ◽  
B. Melichar
Keyword(s):  
Pattern Matching ◽  
Data Structures ◽  
Input Pattern ◽  
Pushdown Automaton ◽  
Ordered Trees ◽  
Tree Pattern ◽  
Tree Patterns ◽  
Tree Pattern Matching ◽  
Ordered Tree ◽  
Pushdown Automata

Trees are one of the fundamental data structures used in Computer Science. We present a new kind of acyclic pushdown automata, the tree pattern pushdown automaton and the nonlinear tree pattern pushdown automaton, constructed for an ordered tree. These automata accept all tree patterns and nonlinear tree patterns, respectively, which match the tree and represent a full index of the tree for such patterns. Given a tree with n nodes, the numbers of these distinct tree patterns and nonlinear tree patterns can be at most 2n?1 +n and at most (2+v)n?1+2, respectively, where v is the maximal number of nonlinear variables allowed in nonlinear tree patterns. The total sizes of nondeterministic versions of the two pushdown automata are O(n) and O(n2), respectively. We discuss the time complexities and show timings of our implementations using the bit-parallelism technique. The timings show that for a given tree the running time is linear to the size of the input pattern.

TWO RELATED ALGORITHMS FOR ROOT-TO-FRONTIER TREE PATTERN MATCHING

2006 ◽  
Vol 17 (06) ◽  
pp. 1253-1272
Author(s):  
LOEK CLEOPHAS ◽  
KEES HEMERIK ◽  
GERARD ZWAAN
Keyword(s):  
Pattern Matching ◽  
Term Rewriting ◽  
Tree Automata ◽  
Term Rewriting Systems ◽  
Missing Link ◽  
Rewriting Systems ◽  
Tree Pattern ◽  
Tree Pattern Matching

Tree pattern matching (TPM) algorithms on ordered, ranked trees play an important role in applications such as compilers and term rewriting systems. Many TPM algorithms appearing in the literature are based on tree automata. For efficiency, these automata should be deterministic, yet deterministic root-to-frontier tree automata (DRFTAS) are less powerful than nondeterministic ones, and no root-to-frontier TPM algorithm using a DRFTA has appeared so far. Hoffmann & O'Donnell presented a root-to-frontier TPM algorithm based on an Aho-Corasick automaton recognizing tree stringpaths. No relationship between this algorithm and algorithms using tree automata has however been described. We show that a specific DRFTA can be used for stringpath matching in a root-to-frontier TPM algorithm. This new algorithm provides a missing link between TPM algorithms using stringpath automata and those using tree automata. We also investigate the correspondence between the automata used by the two algorithms.

TREE-BASED 2D INDEXING

2011 ◽  
Vol 22 (08) ◽  
pp. 1893-1907
Author(s):  
JAN ŽĎÁREK ◽  
BOŘIVOJ MELICHAR
Keyword(s):  
Pattern Matching ◽  
Tree Representation ◽  
Text Indexing ◽  
New Approach ◽  
Tree Pattern ◽  
2D Pattern ◽  
Tree Pattern Matching ◽  
Linear Text ◽  
Pushdown Automata ◽  
String Indexing

A new approach to the 2D pattern matching and specifically to 2D text indexing is proposed. A transformation of a 2D text into the form of a tree is presented. It preserves the context of each element of the 2D text. The tree can be linearised using the prefix notation into the form of a string (a linear text) and the pattern matching is performed in this text. Pushdown automata indexing the 2D text are constructed over the tree representation. They allow to search for 2D prefixes, 2D suffixes, and 2D factors of the 2D text in time proportional to the size of the representation of a 2D pattern. This result achieves the properties analogous to the results obtained in tree pattern matching and string indexing.

PATTERN MATCHING CODE MINIMIZATION IN REWRITING-BASED PROGRAMMING LANGUAGES

2002 ◽  
Vol 13 (06) ◽  
pp. 873-887
Author(s):  
NADIA NEDJAH ◽  
LUIZA DE MACEDO MOURELLE
Keyword(s):  
Programming Languages ◽  
Pattern Matching ◽  
Term Rewriting ◽  
Directed Acyclic Graphs ◽  
Tree Automaton ◽  
Minimal Tree ◽  
Term Rewriting Systems ◽  
Rewriting Systems ◽  
Acyclic Graphs ◽  
Space Requirements

We compile pattern matching for overlapping patterns in term rewriting systems into a minimal, tree matching automata. The use of directed acyclic graphs that shares all the isomorphic subautomata allows us to reduce space requirements. These are duplicated in the tree automaton. We design an efficient method to identify such subautomata and avoid duplicating their construction while generating the dag automaton. We compute some bounds on the size of the automata, thereby improving on previously known equivalent bounds for the tree automaton.

Extended XML Tree Pattern Matching: Theories and Algorithms

2011 ◽  
Vol 23 (3) ◽  
pp. 402-416 ◽  
Author(s):  
Jiaheng Lu ◽  
Tok Wang Ling ◽  
Zhifeng Bao ◽  
Chen Wang
Keyword(s):  
Pattern Matching ◽  
Tree Pattern ◽  
Tree Pattern Matching
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