Simulate nondeterministic automatons

src/editor/mapper.ts

@@ -1,7 +1,7 @@
 import { Graph } from './d3/graph.ts';
 
 type State = {
-  transitions: Record<string, number>;
+  transitions: Record<string, number[]>;
   start?: boolean;
   accepting?: boolean;
 };
@@ -19,8 +19,10 @@ export function createGraph(states: State[]): Graph {
   }
   for (let i = 0; i < states.length; i++) {
     const state = states[i];
-    for (const [letter, target] of Object.entries(state.transitions)) {
-      graph.createLink(i, target, letter);
+    for (const [letter, targets] of Object.entries(state.transitions)) {
+      for (const target of targets) {
+        graph.createLink(i, target, letter);
+      }
     }
   }
   return graph;
@@ -43,7 +45,10 @@ export function createStateList(graph: Graph): State[] {
     const source = reduced[link.source.id];
     const target = reduced[link.target.id];
     for (const label of link.transition.split('')) {
-      states[source].transitions[label] = target;
+      if (!states[source].transitions[label]) {
+        states[source].transitions[label] = [];
+      }
+      states[source].transitions[label].push(target);
     }
   }
   return states;

src/examples.js

@@ -1,6 +1,6 @@
 /**
  * @typedef State
- * @property {Object.<string, number>} transitions
+ * @property {Object.<string, number[]>} transitions
  * @property {boolean} [start]
  * @property {boolean} [accepting]
  */
@@ -9,46 +9,46 @@
  * @type {State[]}
  */
 export const STARTS_ENDS_A = [
-  { transitions: { a: 1, b: 3 } },
-  { transitions: { a: 2, b: 1 } },
-  { transitions: { a: 2, b: 1 }, accepting: true },
-  { transitions: { a: 3, b: 3 } },
+  { transitions: { a: [1], b: [3] } },
+  { transitions: { a: [2], b: [1] } },
+  { transitions: { a: [2], b: [1] }, accepting: true },
+  { transitions: { a: [3], b: [3] } },
 ];
 
 /**
  * @type {State[]}
  */
 export const STARTS_BB = [
-  { transitions: { a: 3, b: 1 } },
-  { transitions: { a: 3, b: 2 } },
-  { transitions: { a: 2, b: 2 }, accepting: true },
-  { transitions: { a: 3, b: 3 } },
+  { transitions: { a: [3], b: [1] } },
+  { transitions: { a: [3], b: [2] } },
+  { transitions: { a: [2], b: [2] }, accepting: true },
+  { transitions: { a: [3], b: [3] } },
 ];
 
 /**
  * @type {State[]}
  */
 export const EXACTLY_ONE_B = [
-  { transitions: { a: 0, b: 1 } },
-  { transitions: { a: 1, b: 2 }, accepting: true },
-  { transitions: { a: 2, b: 2 } },
+  { transitions: { a: [0], b: [1] } },
+  { transitions: { a: [1], b: [2] }, accepting: true },
+  { transitions: { a: [2], b: [2] } },
 ];
 
 /**
  * @type {State[]}
  */
 export const ODD_NUMBER_OF_A = [
-  { transitions: { a: 1, b: 0 } },
-  { transitions: { a: 0, b: 1 }, accepting: true },
+  { transitions: { a: [1], b: [0] } },
+  { transitions: { a: [0], b: [1] }, accepting: true },
 ];
 
 /**
  * @type {State[]}
  */
 export const ENDS_WITH_TWO_B = [
-  { transitions: { a: 0, b: 1 } },
-  { transitions: { a: 0, b: 2 } },
-  { transitions: { a: 0, b: 2 }, accepting: true },
+  { transitions: { a: [0], b: [1] } },
+  { transitions: { a: [0], b: [2] } },
+  { transitions: { a: [0], b: [2] }, accepting: true },
 ];
 
 export const AUTOMATONS = {

src/fsm.js

@@ -47,7 +47,7 @@ export function openAutomaton(states, editable = false) {
    */
   function updateUIState() {
     wordInput.value = builder;
-    if (state === -1 || states.length === 0 || !states[state].accepting) {
+    if (typeof Array.from(state).find((state) => states[state].accepting) === 'undefined') {
       light.classList.remove(IS_VALID);
       light.classList.add(IS_INVALID);
     } else {
@@ -55,8 +55,10 @@ export function openAutomaton(states, editable = false) {
       light.classList.add(IS_VALID);
     }
     graph.forEach((node) => node.active = false);
-    if (state in graph.nodes) {
-      graph.nodes[state].active = true;
+    for (const s of state) {
+      if (s in graph.nodes) {
+        graph.nodes[s].active = true;
+      }
     }
     viewer.restart();
   }
@@ -79,11 +81,16 @@ export function openAutomaton(states, editable = false) {
    * @param {string} letter
    */
   function step(letter) {
-    if (state === -1) {
-      return;
-    }
+    /** @type {number[]} */
+    const newStates = [];
     builder += letter;
-    state = states[state].transitions[letter] ?? -1;
+    for (const s of state) {
+      if (s in states) {
+        const transitions = states[s].transitions[letter];
+        newStates.push(...transitions);
+      }
+    }
+    state = newStates;
     updateUIState();
   }
 
@@ -126,8 +133,17 @@ export function openAutomaton(states, editable = false) {
 
 /**
  * @param {import('./examples.js').State[]} states
+ * @returns {number[]}
  */
 function findStart(states) {
-  let state = states.findIndex(state => state.start);
-  return Math.max(state, 0);
+  const starts = [];
+  for (let i = 0; i < states.length; i++) {
+    if (states[i].start) {
+      starts.push(i);
+    }
+  }
+  if (starts.length === 0) {
+    starts.push(0);
+  }
+  return starts;
 }