Recursively check for epsilon closure states (#21)

src/js/fsa/fsa.js

@@ -1,4 +1,5 @@
 import { UnknownStateError, UnknownSymbolError } from '../util/errors.js'
+import { removeDuplicates } from '../util/array.js'
 
 export default class FSA {
     /**
@@ -114,14 +115,23 @@ export default class FSA {
      * @param {String} fromState The label of the state to find epsilon-reachable states from
      * @returns {Array} The array of states that can be reached via an ε-transition
      */
-    getEpsilonClosureStates (fromState) {
+    getEpsilonClosureStates (fromState, checkedStates = []) {
         if (!this.states.includes(fromState)) throw new UnknownStateError(fromState)
 
+        // Ensure fromState has any epsilon transitions
         if (!this.transitions[fromState] || !this.transitions[fromState]['ε']) {
             return [fromState]
-        } else {
-            return [fromState, ...this.transitions[fromState]['ε']]
         }
+
+        const toStates = this.transitions[fromState]['ε']
+
+        // Recursively check for epsilon transitions
+        // Avoid infinite loop by omitting already-checked states
+        const allEpsilonClosureStates = toStates
+            .filter(s => checkedStates.indexOf(s) === -1)
+            .map(s => this.getEpsilonClosureStates(s, [...checkedStates, ...toStates]))
+
+        return removeDuplicates([fromState, ...allEpsilonClosureStates].flat())
     }
 
     /**
@@ -151,7 +161,6 @@ export default class FSA {
             }
         }
 
-        // Remove duplicate entries by spreading a set
-        return [...new Set(list)].sort()
+        return removeDuplicates(list)
     }
 }

src/js/fsa/nfa_converter.js

@@ -1,4 +1,5 @@
 import FSA from './fsa.js'
+import { removeDuplicates } from '../util/array.js'
 
 export default class NFAConverter {
     /**
@@ -83,8 +84,7 @@ export default class NFAConverter {
             list = this.getUnreachableStates(tempDFA, list.concat(nodesWithoutIncomingEdges))
         }
 
-        // Remove duplicates from the list by spreading it as a Set
-        return [...new Set(list)]
+        return removeDuplicates(list)
     }
 
     /**
@@ -160,7 +160,7 @@ export default class NFAConverter {
 
         // The new start state is the states that are reachable from the original start state
         // e.g. '1' has an ε-transition to '3'; therefore, the new start state is '1,3'
-        const startState = [...new Set(this.nfa.getEpsilonClosureStates(this.nfa.startState))].sort().join(',')
+        const startState = removeDuplicates(this.nfa.getEpsilonClosureStates(this.nfa.startState)).join(',')
 
         // The new list of accept states are any states from the powerset with the original accept state in them
         // e.g. '1' is the accept state; therefore, '1', '1,2', '1,3', and '1,2,3' are accept states
@@ -208,8 +208,7 @@ export default class NFAConverter {
                 reachableStates = reachableStates.concat(this.nfa.getReachableStates(s, symbol))
             })
 
-            // Remove any duplicates and sort the states alphabetically
-            reachableStates = [...new Set(reachableStates)].sort()
+            reachableStates = removeDuplicates(reachableStates)
 
             // Remove Ø if the state has other possibilites
             if (reachableStates.some(e => e !== 'Ø')) {

src/js/fsa/visual_fsa.js

@@ -1,5 +1,6 @@
 import EventHandler from '../util/event_handler.js'
 import { UnknownStateError } from '../util/errors.js'
+import { removeDuplicates } from '../util/array.js'
 import FSA from './fsa.js'
 import Location from '../canvas/location.js'
 import EditNodeMenu from '../elements/edit_node_menu.js'
@@ -234,7 +235,7 @@ export default class VisualFSA extends EventHandler {
                 if (symbol !== 'ε') { alphabet.push(symbol) }
             }
         }
-        this.fsa.alphabet = [...new Set(alphabet)].sort()
+        this.fsa.alphabet = removeDuplicates(alphabet)
     }
 
     /**
@@ -259,8 +260,8 @@ export default class VisualFSA extends EventHandler {
         fromNode.transitionText[to].push(symbol)
 
         // Remove duplicates in case the user somehow added two of the same transitions
-        fromNode.transitionText[to] = [...new Set(fromNode.transitionText[to])].sort()
-        this.fsa.transitions[from][symbol] = [...new Set(this.fsa.transitions[from][symbol])].sort()
+        fromNode.transitionText[to] = removeDuplicates(fromNode.transitionText[to])
+        this.fsa.transitions[from][symbol] = removeDuplicates(this.fsa.transitions[from][symbol])
 
         this.updateAlphabet()
         this.dispatchEvent('change')

src/js/test/fsa.test.js

@@ -17,7 +17,7 @@ describe('FSA 1', () => {
         '3': {
             'a': ['1'],
             'b': undefined,
-            'ε': undefined
+            'ε': ['2']
         }
     }, '1', ['1'])
 
@@ -29,18 +29,18 @@ describe('FSA 1', () => {
     })
 
     it('should get epsilon closure states', done => {
-        fsa.getEpsilonClosureStates('1').should.eql(['1', '3'])
+        fsa.getEpsilonClosureStates('1').should.eql(['1', '2', '3'])
         fsa.getEpsilonClosureStates('2').should.eql(['2'])
-        fsa.getEpsilonClosureStates('3').should.eql(['3'])
+        fsa.getEpsilonClosureStates('3').should.eql(['2', '3'])
         done()
     })
 
     it('should get reachable states', done => {
         fsa.getReachableStates('1', 'a').should.eql(['Ø'])
         fsa.getReachableStates('1', 'b').should.eql(['2'])
         fsa.getReachableStates('2', 'a').should.eql(['2', '3'])
-        fsa.getReachableStates('2', 'b').should.eql(['3'])
-        fsa.getReachableStates('3', 'a').should.eql(['1', '3'])
+        fsa.getReachableStates('2', 'b').should.eql(['2', '3'])
+        fsa.getReachableStates('3', 'a').should.eql(['1', '2', '3'])
         fsa.getReachableStates('3', 'b').should.eql(['Ø'])
         done()
     })

src/js/test/visual_fsa.test.js

@@ -165,78 +165,4 @@ describe('Visual FSA', () => {
 
         done()
     })
-
-    it('should step backward in the DFA conversion', done => {
-        const visualNFA = new VisualFSA(new DraggableCanvas('#nfa'), false)
-
-        visualNFA.addNode('1', new Location(100, 100))
-        visualNFA.addNode('2', new Location(100, 100))
-        visualNFA.setStartState('1')
-        visualNFA.addAcceptState('1')
-        visualNFA.addTransition('1', '2', 'b')
-        visualNFA.addTransition('1', '1', 'a')
-        visualNFA.addTransition('2', '1', 'a')
-        visualNFA.addTransition('2', '2', 'b')
-
-        const visualDFA = new VisualFSA(new DraggableCanvas('#dfa'), true)
-        const converter = new NFAConverter(visualNFA.fsa)
-
-        for (let i = 0; i < 10; i++) {
-            const [newDFA, step] = converter.stepForward()
-            visualDFA.performStep(step, newDFA)
-        }
-
-        visualDFA.fsa.states.should.eql(['1', '2', '1,2'])
-        visualDFA.fsa.startState.should.eql('1')
-        visualDFA.fsa.acceptStates.should.eql(['1', '1,2'])
-        visualDFA.fsa.transitions.should.eql({
-            '1': { a: ['1'], b: ['2'] },
-            '2': { a: ['1'], b: ['2'] },
-            '1,2': { a: ['1'], b: ['2'] }
-        })
-
-        {
-            const [prevDFA, step] = converter.stepBackward()
-            visualDFA.undoStep(step, prevDFA)
-        }
-
-        visualDFA.fsa.states.should.eql(['1', '2', '1,2', 'Ø'])
-        visualDFA.fsa.startState.should.eql('1')
-        visualDFA.fsa.acceptStates.should.eql(['1', '1,2'])
-        visualDFA.fsa.transitions.should.eql({
-            'Ø': { a: ['Ø'], b: ['Ø'] },
-            '1': { a: ['1'], b: ['2'] },
-            '2': { a: ['1'], b: ['2'] },
-            '1,2': { a: ['1'], b: ['2'] }
-        })
-
-        for (let i = 0; i < 2; i++) {
-            const [newDFA, step] = converter.stepForward()
-            visualDFA.performStep(step, newDFA)
-        }
-
-        visualDFA.fsa.states.should.eql(['1', '2'])
-        visualDFA.fsa.startState.should.eql('1')
-        visualDFA.fsa.acceptStates.should.eql(['1'])
-        visualDFA.fsa.transitions.should.eql({
-            '1': { a: ['1'], b: ['2'] },
-            '2': { a: ['1'], b: ['2'] }
-        })
-
-        {
-            const [prevDFA, step] = converter.stepBackward()
-            visualDFA.undoStep(step, prevDFA)
-        }
-
-        visualDFA.fsa.states.should.eql(['1', '2', '1,2'])
-        visualDFA.fsa.startState.should.eql('1')
-        visualDFA.fsa.acceptStates.should.eql(['1', '1,2'])
-        visualDFA.fsa.transitions.should.eql({
-            '1': { a: ['1'], b: ['2'] },
-            '2': { a: ['1'], b: ['2'] },
-            '1,2': { a: ['1'], b: ['2'] }
-        })
-
-        done()
-    })
 })

src/js/util/array.js

@@ -0,0 +1,9 @@
+/**
+ * Remove duplicate elements from the array and sort it
+ *
+ * @param {Array} arr The array to remove duplicate elements from
+ * @returns {Array} The deduplicated array
+ */
+export function removeDuplicates (arr) {
+    return [...new Set(arr)].sort()
+}