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1.0.0 • Public • Published


A lexical analysis / regular expression engine written in TypeScript

Get started

Install with NPM or Yarn

  • With NPM

    $ npm install lxa --save
  • With Yarn

    $ yarn add lxa

Quick starting example

Let's get started by generating a regular expression checker, testing whether a string is of the language of /(a|b)*cd?/ using lxa.

Tips: You will see there are concepts of NFAs and DFAs in the example code. Don't be worried about that since using lxa does not require the prerequisite knowledge of NFAs (Non-deterministic Finite Automata) and DFAs (Deterministic Finite Automata). It's not hard for you to build your own lexical analyzer or regular expression tools following this guide. Understanding those concepts helps you acquire a deeper understanding of the lxa's principle though.

The expression of (a|b)*cd? consists of three parts, which also consist of smaller units, and so on. The following describes all the parts of the entire expression.

The entire expression is the concatenation of the following three expressions

  • (a|b)*

    • which is the closure of (a|b)

      • which is the union of a and b
  • A single character of c

  • d?

    • The concatenation of single character d and empty string (We mark empty string as ε (epsilon)
  1. First, we need to create states for each part of the expression and combine them together.

    import { stateOps, epsilon } from 'lxa';
    const {  SingleInputState,  UnionState, ClosureState } = stateOps;
    // state for single character 'a' and 'b'
    const state_for_a = new SingleInputState('a');
    const state_for_b = new SingleInputState('b');
    // and generate the union of 'a' and 'b', (a|b)
    const union_of_a_and_b = new UnionState(a, b);
    // and then the closure `(a|b)*`
    const union_of_a_and_b_closure = new ClosureState(union_of_a_and_b);
    // and concatenate `(a|b)*` with c
    const concat_with_c = new ConcatState(union_of_a_and_b_closure, new SingleInputState('c'));
    // Before we generate the final expression,
    // we generate the union of 'd' and empty string,
    // representing `d?` or `d|ε`
    const d_or_empty = new UnionState(
      new SingleInputState('d'),
      new SingleInputState(epsilon),
      // `true` means this is the final accepted state.
      // Refer to API doc for more detail.
    // Finally, we concatenate them all
    const final = new ConcatState(concat_with_c, d_or_empty);
  2. Generate a DFA for testing.

    import { NFA } from 'lxa';
    const dfa = new NFA(final).toDFA();
    dfa.test('aaac'); // true
    dfa.test('abcd') // true
    dfa.test('bbbcd') // true
    dfa.test('ad') // false

It is verbose to union or concatenate multiple states because we need to nest those states in a very deep hierarchy, especially when the expression is complicated. We have provided you with two util functions concatMultipleStates(), unionMultipleStates() to union or concatenate multiple states such that we don't have to nest them all.

import { concatMultipleStates } from 'lxa';
// This is much concise
const final = concatMultipleStates(
  new SingleInputState('c'),



epsilon is a singleton object representing an empty string. It can be used as the argument for input of the StateOp's constructor.



This is the base class. Please do not instantiate it explicitly. You can use it as a type notation for TypeScript. The following classes are subclasses of StateOp.


constructor SingleInputState(input: InputType, accepted?: boolean): SingleInputState

  • inputType is either a string type or the epsilon object
  • accepted indicates whether the current state is accepted or not. If the current state is accepted and there is no more input string, the whole regular expression is accepted. Refer to the the explanation for NFAs and DFAs for more details about the accepted state. Default to false.


constructor ConcatState(a: StateOp, b: StateOp): ConcatState

Concatenates two states. Use concatMultipleStates() for a shorthand of concatenating more states.


constructor UnionState(a: StateOp, b: StateOp, accepted?: boolean): UnionState

Unions two states. Use Use unionMultipleStates() for a shorthand of uniting more states.

  • accepted, ditto


constructor ClosureState(a: StateOp, accepted?: boolean): ClosureState

Generates the closure of a state.

  • a is the input state to use to generate the closure
  • accepted, ditto


function concatMultipleStates(...states: StateOp[]): StateOp

Concatenates multiple states together. Shorthand for nesting constructors of stateOps.ConcatState


function unionMultipleStates({states, accepted}): StateOp

Unites multiple states together. Shorthand for nesting constructors of stateOps.UnionState

  • states is an array of StateOp instances
  • accepted, ditto


NFA constructor

constructor NFA(state: StateOp): NFA


NFA.prototype.toDFA.toDFA(): DFA

Returns a DFA instance generating from the NFA instance caller



DFA.prototype.test(input: string): boolean

Checks if the input string is of the expression language


Under the MIT License.


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