dfa

Compiles a regular expression like syntax to fast deterministic finite automata. Useful for pattern matching against non-string sequences.

Example

This example matches Hangul syllables. The symbols defined in the machine are Unicode character categories which could be mapped from code points.

Machine definition:

# define symbols
X   = 0; # Other character
L   = 1; # Leading consonant
V   = 2; # Medial vowel
T   = 3; # Trailing consonant
LV  = 4; # Composed <LV> syllable
LVT = 5; # Composed <LVT> syllable
M   = 6; # Tone mark

# define variables
decomposed = L V T?;
partial = LV T?;
composed = LVT;

# define main state machine pattern
main = (decomposed | partial | composed) M?;

Visualized, the machine looks like this (double circles are accepting states):

Compiling and using the machine:

import compile from 'dfa/compile';
import fs from 'fs';

let stateMachine = compile(fs.readFileSync('hangul.machine', 'utf8'));

// find matches
for (let [startIndex, endIndex] of stateMachine.match([0, 1, 2, 3, 0, 4, 6]) {
  console.log('match:', startIndex, endIndex);
}

Output:

match: 1 3
match: 5 6

Syntax

A state machine file contains a list of assignment statements. Comments are also allowed and are started with the # character. Each statement is an assignment of a variable name to a value or expression. Assigning a variable to a number produces a symbol, which is added to the state machine's alphabet. Assigning a variable to an expression allows for substitutions into later expressions. The special main variable should always be assigned to at the end of the file, and is the final expression that will be compiled.

A subset of common regular expression syntax is supported. A list of operators and their precedence is below. Operators with the same precedence are evaluated left to right.

| Precedence | Syntax | Type | Meaning | | ---------- | ---------- | --------------| ------------------------------------------ | | 1 | a \| b | Alternation | Matches either a or b | | 2 | a b | Concatenation | Matches a followed by b | | 3 | a* | Repetition | Matches zero or more occurrences of a | | 3 | a+ | Repetition | Matches one ore more occurrences of a | | 3 | a? | Optional | Matches zero or one occurrence of a | | 3 | a{n} | Repetition | Matches exactly n occurrences of a | | 3 | a{n,} | Repetition | Matches n or more occurrences of a | | 3 | a{,n} | Repetition | Matches up to n occurrences of a | | 3 | a{n,m} | Repetition | Matches n to m occurrences of a | | 4 | t:<expr> | Tag | Tags the following expression with tag t | | 5 | (<expr>) | Grouping | Groups an expression |

License

MIT