🌁 Nondeterministic Finite State Automata for Java (in plain English: flowcharts with multiple possible outcomes)
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Nondeterministic finite state automata

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This is a library that provides an implemention of nondeterminstic finite state automata (NFAs) in Java. You can think of NFAs as flowcharts: you are in a state, take some action, and arrive in a new state. The action can produce a side effect, such as writing a string to a tape.


Download the latest JAR or grab from Maven:


or Gradle:

compile 'org.leibnizcenter:nfa:1.0.0'


There are already a bunch of libraries out there which work with deterministic finite state automata (DFAs), and there is a well-known result in automata theory which says that for any language recognized by an NFA, we can construct a DFA which recognizes the same language.

So why not just use DFAs? Two reasons:

On a side note, Allauzen & Mohri have described efficient algorithms for determining when a transducer is in fact determinizable, and this would be a nice feature to implement.

Current features

  • Arbitrary input tokens, and arbitrary side effect to state transitions. For example we may implement a finite state transducer by taking strings as input tokens and writing some output string to tape as a side effect.
  • Compute possible transition paths in polynomial time! Using a forward-backward-like algorithm, we can compute all paths through automaton A originating from state S, given input I all possible paths in O(|S| * |I| * |A|).
  • Transition paths can be accessed through a Spliterator: Java 8 streaming APIs can automatically branch transition paths on states where one action may lead to multiple result states.


Here is a simple example of a parking meter that takes money:

public class ParkingMeter {
     * How much money is in the machine
    private int ¢¢¢;

    public static void main(String[] args) {
        // Run example
        new ParkingMeter().run();
    public void run() {
        // Say we can buy parking for 100 cents

        // Define some actions
        CoinDrop drop25cents = new CoinDrop(25);
        CoinDrop drop50cents = new CoinDrop(50);

        // Define our NFA
        NFA<PayState, CoinDrop> nfa = new NFA.Builder<PayState, CoinDrop>()
                .addTransition(PAYED_0, drop25cents, PAYED_25)
                .addTransition(PAYED_0, drop50cents, PAYED_50)
                .addTransition(PAYED_25, drop25cents, PAYED_50)
                .addTransition(PAYED_25, drop50cents, PAYED_75)
                .addTransition(PAYED_50, drop25cents, PAYED_75)
                .addTransition(PAYED_50, drop50cents, PAYED_0)
                .addTransition(PAYED_75, drop25cents, PAYED_0)
                .addTransition(PAYED_75, drop50cents, PAYED_0) // Payed too much... no money back!

        // Apply action step-by-step
        Collection<State> endStates1 = nfa.start(PAYED_0)

        // Or apply actions in bulk (this makes calculations of the possible paths more efficient, but it doesn't matter if we iterate over all transitions anyway)
        Collection<State> endStates2 = nfa.apply(PAYED_0, new LinkedList<>(Arrays.asList(drop50cents, drop25cents, drop50cents, drop25cents)))

        System.out.println("Today earnings: ¢" + ¢¢¢ + ".");
    private class CoinDrop implements Event<PayState> {
        final int ¢;
        CoinDrop(int value) {
            this.¢ = value;
        public void accept(PayState from, PayState to) {
            System.out.println("Bleep Bloop. Added ¢" + ¢ + " to ¢" + from.¢ + ". ");
            if (to.¢ <= 0 || to.¢ >= 100) System.out.println("You may park. Good day.");
                System.out.println("You have paid ¢" + to.¢ + " in total. Please add ¢" + (100 - to.¢) + " before you may park.");
            ¢¢¢ += this.¢;
        public String toString() {
            return "¢" + ¢;
    enum PayState implements State {
        PAYED_0(0), PAYED_25(25), PAYED_50(50), PAYED_75(75);
        public int ¢;
        PayState(int ¢) {
            this.¢ = ¢;