Indexing ordered trees for (nonlinear) tree pattern matching by 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.

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On Tree Pattern Matching by Pushdown Automata

Acta Polytechnica ◽

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.

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Optimal Regular Tree Pattern Matching Using Pushdown Automata

Lecture Notes in Computer Science - Foundations of Software Technology and Theoretical Computer Science ◽

10.1007/978-3-540-49382-2_11 ◽

1998 ◽

pp. 122-133 ◽

Cited By ~ 3

Author(s):

Maya Madhavan ◽

Priti Shankar

Keyword(s):

Pattern Matching ◽

Regular Tree ◽

Tree Pattern ◽

Tree Pattern Matching ◽

Pushdown Automata

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A Note on Linear Time Simulation of Deterministic Two-Way Pushdown Automata

DAIMI Report Series ◽

10.7146/dpb.v6i75.6492 ◽

1977 ◽

Vol 6 (75) ◽

Author(s):

Neil D. Jones

Keyword(s):

Pattern Matching ◽

Data Structures ◽

Linear Time ◽

Random Access ◽

Simulation Algorithm ◽

Pushdown Automaton ◽

Matching Problems ◽

Time Result ◽

Time Simulation ◽

Pushdown Automata

<p>Cook has shown that any deterministic two-way pushdown automaton could be simulated by a uniform-cost random access machine in time O(n) for inputs of length n. The result was of interest because such a machine is a natural model for a variety of backtracking algorithms, particularly as used in pattern matching problems. The linear time result was surprising because of the fact that such machines may run as many as 2n steps before halting; similar problems with 'combinatorial explosions' are well known to occur in applications of backtracking. Cook's result inspired the development of a number of efficient pattern matching algorithms.</p><p>However, it is impractical to use Cook's algorithm directly to do pattern matching, since it involves a large constant time factor and much storage. The purpose of this note is to present an alternate, simpler simulation algorithm which involves consideration only of the configurations actually reached by the automaton. It can be expected to run faster and use less storage (depending on the data structures used), thus bringing Cook's result a step closer to practical utility.</p>

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TREE-BASED 2D INDEXING

International Journal of Foundations of Computer Science ◽

10.1142/s0129054111009100 ◽

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.

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