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Simple Java Regular Expression Implementation

Introduction

Regular Expressions is an amazing tool that makes our lives easier. The power it gives is well perceived thus it is supported by many programming and scripting languages. Power of regular expressions comes from another great mathematical tool: deterministic or non-deterministic finite automata. NFA/DFA is an interesting topic covered in Formal Languages and Automata Theory lectures which is supposed to be taken by all Computer Science graduates.

This article covers a simple NFA implementation of regular expressions. Thompson NFA algorithm, which is referenced in Regular Expression Matching Can Be Simple and Fast article, is used in implementation.

Implementation


Grammar

Implementation uses the following Backus-Naur Form grammar which is a subset of the grammar presented in A Grammar for Regular Expressions.

<regex>         ::= <simple-regex> | <simple-regex>|<regex>
<simple-regex>  ::= <term> | <term><simple-regex>
<term>          ::= <factor> | <factor>* | <factor>?
<factor>        ::= <character> | . | (<regex>)
<character>     ::= <any char except '(', ')', '?', '*', '+', '|'>


Design 

Interpreter pattern is exploited to construct NFA structure. Fragments within angle brackets are non-terminal symbols while fragments without angle brackets represents terminal symbols. Each symbol has a corresponding class either rooted by TerminalState or NonTerminalState interfaces. NonTerminalState objects are containers for Terminal and Non-Terminal state objects. NFA is constructed as a tree of Terminal and Non-Terminal State objects in which Terminal states are essentially leaves of the tree. Each State object has a (compulsorily Terminal) Start State and a list of end states which connects the state object to consequent state object.

Given a regular expression complying with the grammar specified above, firstly a NFA is constructed. Then a desired input sequence is fed to NFA. After all characters are processed by NFA if NFA is at an “accept state” then it is said that input sequence belongs to this NFA and test method returns true. If NFA is not at an “accept state” input sequence does not belong to this NFA and test method returns false.

Unlike the reference implementation which uses postfix notation and explicit concatenation symbols, this implementation uses infix notation and does not uses explicit concatenation symbols.

NFA Construction

-          Construction process uses a State stack to parse expression. Once construction is over stack is no longer used.
-          If a terminal symbol is read it is pushed to syntax as LabeledTerminalState.
-          If a left parentheses is read it is also pushed to stack as LabeledTerminalState to mark the start of parentheses expression.
-          If a right parentheses is read all items in the stack is popped and concatenated until left parentheses is popped from stack.
-          Concatenation is done using ConcatenationState objects which takes two State objects as input. Basically connects all next pointers at the end lists of first state to start state of second state.
-          Alteration, One or More, Zero or More and Zero or One symbols are handled in the same way it is explained in implementation section of  Regular Expression Matching Can Be Simple and Fast article. Fragments in the reference article roughly corresponds to Non-Terminal States in this writing. Split states in reference article roughly corresponds to UnlabeledTerminalState in this implementation. It is advised to read the reference article for a better explanation whereas it is advised to have look at the Java implementation that can be downloaded from below which  is easier to read and hopefully to understand.

Input Test

Once NFA is constructed it can be used to test the conformity of any input sequence. Input sequence is read char by char and NFA is executed. Each execution starts with a current state list which contains the terminal state objects that NFA is currently in. Each execution populates next state list which contains the states in which NFA will be, in next execution. Basically execution abstracts the process of checking labeled terminal states against current char. If char matches current state next labeled terminal states are put to next state list, which may require following unlabeled terminal states until labeled states are reached.

Each execution step has an execution step ID to differentiate execution steps from each other and more importantly to avoid multiple addition of terminal states to next state list. Otherwise some expressions may be added repeatedly until thread stack is overflowed.

When all chars from input sequence is read and executed, execution stops. If next list contains accept state test method returns true.

Summary


Regular expression implementation can be quiet simple. It is possible to download source files from here.
Feel free to share your comments to http://el-harezmi.blogspot.com on design and any typos, incorrect or inaccurate expressions you see.

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