Regex Processing Framework

1. Revision History
2. About This Document
   1. Purpose
   2. Intended Audience
   3. Documentation Conventions
3. Introduction to Pattern Matching
4. AbstractSet Interface
   1. Characteristics
   2. Methods Used
   3. Class Hierarchy
   4. Optimizations
5. Usage Examples
6. References

Revision History

Version	Version Information	Date
Initial version	Nadya Morozova, Nikolay Kuznetsov: document created.	December 16, 2005
Formatting update	Nadya Morozova	September 21, 2006

About This Document

Purpose

This document describes the java.util.regex package delivered as part of the Harmony classlibrary project. This document provides an overview of the overall architecture with focus on the aspects improving performance.

Intended Audience

The target audience for the document includes a wide community of engineers interested in using regular expression package and in further work with the product to contribute to its development. The document assumes that readers are familiar with Regular expressions [1, 2, 3], finite automata theory [4], basic compiler techniques [4] and the Java* programming language [5].

Documentation Conventions

This document uses the unified conventions for the Harmony documentation kit.

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Introduction to Pattern Matching

To analyze text in search of sequences matching preset patterns, you can choose from a variety of techniques, such as the wide-spread regular expressions (RE) [1], exact string matching, for example, the Boyer-Moore algorithm (BM) [6], and others. However, the RE engine is rather complex, and significantly impacts performance, whereas the exact string matching techniques have a limited application.

For example, the regular expression .*world is used to find the last instance of world in a sentence. The BM string searching algorithm is more appropriate for solving the task than the RE technique, and is more effective from the performance perspective. To optimize using pattern matching techniques with different tasks, Harmony provides a unified interface that applies to any part of a regular expression, including the whole expression.

In terms of the Finite Automata theory, which is the basis of regular expression processing, a part of regular expression is a node. The Harmony regex framework treats every distinctive part of a regular expression and the whole expression as a node. Each node implements the unified interface adjusted for a specific technique. For instance, for the regular expression in the example, the Harmony framework includes a special class SequenceSet, which has a unified interface called AbstractSet, and implements the Boyer-Moore algorithm in searching for a word.

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AbstractSet Interface

The key feature of the Harmony regex framework the single super interface, AbstractSet, shared by all types of nodes. Individual nodes are independent, so that every node of the automaton incorporates its own find-match algorithm optimized for a specific type of nodes. You can use methods implemented in the AbstractSet interface subclasses or override these methods to use your own more efficient algorithm.

Characteristics

The AbstractSet interface has the following key characteristics:

• Unified structure: General contract for all nodes including node chains. This enables the framework to support new features and optimizations for a specific construction of RE without impacting other parts of the framework.
• Simplicity: Every node of an automaton is simple and handles a specific optimization or functionality. The resulting automaton is straight-forward and includes no multi-purpose functionality. To enable support of new functionality, create a new class.

  Note

  Because new features and optimizations are implemented independently, expansion of the framework has no negative impact on the overall performance.

• Independence:The matching and finding procedures are incorporated into the interface and require no external logic. The interface allows using the same find-match methods for all types of nodes, and at the same time enables optimizing the find-match algorithm for individual node types to improve performance.

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Methods Used

The AbstractSet interface defines the matching and finding methods, and the service methods supporting them, as follows.

Service Methods

accept()

Checks whether the current node matches the current string symbol(s) to ensure that the automaton can proceed with the current state. The method returns the number of accepted symbols. This method is designed for nodes representing tokens, which mostly use the default match procedure. To optimize the match procedure for a specific type of token, you only need to override the accept() method, see Example 1.

first()

Checks whether the first symbol of the current node intersects with previous one. If not, then the previous node is quantified possessively without backtrack (the option of restarting the search from the previous position).

next()

Returns the next node of the automaton.

Matching and Finding Methods

matches()

Runs the match procedure starting from the current state. This is the only method you need to override in order to introduce new functionality. By default, the matches() method does the following when working with terms (see Class Hierarchy):

1. Calls the accept() method and proceeds if the method returns a positive value.
2. Calls the match of the next node with the shift obtained from the accept() method.
3. Returns TRUE in case of a successful match.

find()

Checks whether the pattern can match any part of the string in the following way:

1. Finds the next position in the input string, for which the accept() method returns a positive value. If no matches are found, the method terminates and returns a negative value.
2. From this position, runs the matches() method.

findBack()

Does the same as the find() method but starts from the end of the string or from the nearest new-line symbol. This method optimizes the find procedure when the current node of the pattern fits the rest of the string. In such cases, it is necessary to find the last occurrence of the pattern represented by the next node, as in the case of the .*world pattern.

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Class Hierarchy

Figure 1 shows the class hierarchy based on the AbstractSet interface. As mentioned in its description, the whole hierarchy is based on this interface. The other classes of the framework are divided into the following categories:

• Tokens or Leafs (LeafSet in the figure): nodes representing ordinal symbols, substrings, ranges, character classes, and other basic units of regular expressions.
• Quantifiers (QuantifierSet in the figure): set of nodes responsible for quantification of terms. Terms are simple and usually represent only one symbol. Therefore, terms are quantified without recursion, and backtracks are processed on the basis of the underlying pattern length.
• Groups (JointSet in the figure): sets derived from parenthetic constructions. These nodes represent alternations of other sets.
• Group Quantifiers (GroupQuantifier in the figure): special quantifiers over Groups. Because the length of a groups can vary, backtracks require recursion.

Figure 1. Class Hierarchy

Figure 1 displays only the basics of the regex framework. This framework also includes other nodes responsible for different optimizations. For more details, see the comments inlined in code.

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Optimizations

In the current implementation, most optimizations are based on the node representation to improve efficiency of the framework. It is noteworthy that an optimal finite automaton is built during compile time, so that the constructed automaton does not spend additional time on decision-making overhead during match time. The regex framework optimizations improve different aspects, such as:

• Character or String find methods: The methods find() and findBack() of certain nodes use exact pattern matching algorithms, specifically, the Boyer-Moore fast string search algorithm.
• Quantified dot term: This term (.*) covers the rest of the string and can therefore run findBack() from the end of the string. If the findBack() method of the following node implements a special algorithm, the pattern matching speed for this chain increases, otherwise the operation runs at the same speed.
• Quantified non-intersecting states: If the quantified node does not intersect with the first character of the next one, the framework treats the quantifier as the possessive quantifier because no backtracks can occur. Possessive quantification is based on loops instead of recursion and works faster.

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Usage Examples

This part on the document illustrates usage of the Harmony regex framework.

Example 1

This example illustrates using the CharSet class, which includes all nodes accepting characters to create a new type of tokens. For that, the class uses the LeafSet class, which is the basic class for tokens. This example shows that the only method you need to override in order to present a new type of tokens is the accept() method.

class CharSet extends LeafSet {
    ...
    public int accept(int strIndex, CharSequence testString) {
        // checks that the current symbol of the input string is the one this 
        // instance represents and returns 1 (the number of
        // accepted symbols) or -1 if accept fails:
        return (this.ch == testString.charAt(strIndex)) ? 1 : -1;
    }
    ...
}

Example 2

The following example demonstrates independent implementation of the find() method for SequenceSet.

Note

This changes the find procedure for nodes representing character sequences and at the same time does not affect the find-match algorithms of other types of nodes.

class SequenceSet extends LeafSet {
    ...
    protected int indexOf(CharSequence str, int from) {
        // Boyer-Moore algorithm 
        ...
    }
    
    public int find(int strIndex, CharSequence testString,
            MatchResultImpl matchResult) {
        ...
        while (strIndex <= strLength) {
            // call the fast search method instead of default implementation
            strIndex = indexOf(testStr, strIndex);
            if (strIndex < 0) {
                return -1;
            }
            if (next.matches(strIndex + charCount, testString, matchResult) >= 0) {
                return strIndex;
            }
            strIndex++;
        }
        return -1;
    }
    ...
}

Example 3

This example illustrates how to turn the match procedure of the .* patterns into the find procedure, which is potentially faster.

class DotQuantifierSet extends LeafQuantifierSet {
    ...     
    public int matches(int stringIndex, CharSequence testString,
            MatchResultImpl matchResult) {
        ...
        // find line terminator, since .* represented by this node accepts all characters
        // except line terminators 
        int startSearch = findLineTerminator(stringIndex, strLength, testString);
        ...
        // run findBack method of the next node, because the previous 
        // part of the string is accepted by .* and no matter where
        // the next part of pattern is found, the procedure works OK.  
        return next.findBack(stringIndex, startSearch, testString, matchResult);
    }
}

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References

[1] Jeffrey E. F. Friedl., Mastering regular expressions, 2nd Edition., July 2002, O'Reilly, ISBN 0-596-00289-0

[2] McNaughton, R. and Yamada, H. Regular Expressions and State Graphs for Automata, IRA Trans. on Electronic Computers, Vol. EC-9, No. 1, Mar. 1960, pp 39-47.

[3] Thompson, K., Regular Expression search Algorithm, Communication ACM 11:6 (1968), pp. 419-422.

[4] Alfred V. Aho, Ravi Sethi, Jeffrey D. Ullman, Compilers, Principles Techniques and Tools, Addison-Wesley Publishing Company, Inc., 1985, ISBN 0-201-10088-6

[5] Java Technology site, http://java.sun.com

[6] R. Boyer and S. Moore. A fast string searching algorithm. C. ACM, 20:762-772, 1977.

[7] D.E. Knuth, .I. Morris, and V. Pratt. Fast pattern matching in strings. SIAM J on Computing, 6:323-350, 1977.

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