412 lines
No EOL
12 KiB
JavaScript
412 lines
No EOL
12 KiB
JavaScript
/**
|
|
* The MIT License (MIT)
|
|
* Copyright (c) 2017-present Dmitry Soshnikov <dmitry.soshnikov@gmail.com>
|
|
*/
|
|
|
|
'use strict';
|
|
|
|
// DFA minization.
|
|
|
|
/**
|
|
* Map from state to current set it goes.
|
|
*/
|
|
|
|
var _slicedToArray = function () { function sliceIterator(arr, i) { var _arr = []; var _n = true; var _d = false; var _e = undefined; try { for (var _i = arr[Symbol.iterator](), _s; !(_n = (_s = _i.next()).done); _n = true) { _arr.push(_s.value); if (i && _arr.length === i) break; } } catch (err) { _d = true; _e = err; } finally { try { if (!_n && _i["return"]) _i["return"](); } finally { if (_d) throw _e; } } return _arr; } return function (arr, i) { if (Array.isArray(arr)) { return arr; } else if (Symbol.iterator in Object(arr)) { return sliceIterator(arr, i); } else { throw new TypeError("Invalid attempt to destructure non-iterable instance"); } }; }();
|
|
|
|
function _toArray(arr) { return Array.isArray(arr) ? arr : Array.from(arr); }
|
|
|
|
function _toConsumableArray(arr) { if (Array.isArray(arr)) { for (var i = 0, arr2 = Array(arr.length); i < arr.length; i++) { arr2[i] = arr[i]; } return arr2; } else { return Array.from(arr); } }
|
|
|
|
var currentTransitionMap = null;
|
|
|
|
/**
|
|
* Takes a DFA, and returns a minimized version of it
|
|
* compressing some states to groups (using standard, 0-, 1-,
|
|
* 2-, ... N-equivalence algorithm).
|
|
*/
|
|
function minimize(dfa) {
|
|
var table = dfa.getTransitionTable();
|
|
var allStates = Object.keys(table);
|
|
var alphabet = dfa.getAlphabet();
|
|
var accepting = dfa.getAcceptingStateNumbers();
|
|
|
|
currentTransitionMap = {};
|
|
|
|
var nonAccepting = new Set();
|
|
|
|
allStates.forEach(function (state) {
|
|
state = Number(state);
|
|
var isAccepting = accepting.has(state);
|
|
|
|
if (isAccepting) {
|
|
currentTransitionMap[state] = accepting;
|
|
} else {
|
|
nonAccepting.add(state);
|
|
currentTransitionMap[state] = nonAccepting;
|
|
}
|
|
});
|
|
|
|
// ---------------------------------------------------------------------------
|
|
// Step 1: build equivalent sets.
|
|
|
|
// All [1..N] equivalent sets.
|
|
var all = [
|
|
// 0-equivalent sets.
|
|
[nonAccepting, accepting].filter(function (set) {
|
|
return set.size > 0;
|
|
})];
|
|
|
|
var current = void 0;
|
|
var previous = void 0;
|
|
|
|
// Top of the stack is the current list of sets to analyze.
|
|
current = all[all.length - 1];
|
|
|
|
// Previous set (to check whether we need to stop).
|
|
previous = all[all.length - 2];
|
|
|
|
// Until we'll not have the same N and N-1 equivalent rows.
|
|
|
|
var _loop = function _loop() {
|
|
var newTransitionMap = {};
|
|
|
|
var _iteratorNormalCompletion3 = true;
|
|
var _didIteratorError3 = false;
|
|
var _iteratorError3 = undefined;
|
|
|
|
try {
|
|
for (var _iterator3 = current[Symbol.iterator](), _step3; !(_iteratorNormalCompletion3 = (_step3 = _iterator3.next()).done); _iteratorNormalCompletion3 = true) {
|
|
var _set = _step3.value;
|
|
|
|
// Handled states for this set.
|
|
var handledStates = {};
|
|
|
|
var _set2 = _toArray(_set),
|
|
first = _set2[0],
|
|
rest = _set2.slice(1);
|
|
|
|
handledStates[first] = new Set([first]);
|
|
|
|
// Have to compare each from the rest states with
|
|
// the already handled states, and see if they are equivalent.
|
|
var _iteratorNormalCompletion4 = true;
|
|
var _didIteratorError4 = false;
|
|
var _iteratorError4 = undefined;
|
|
|
|
try {
|
|
restSets: for (var _iterator4 = rest[Symbol.iterator](), _step4; !(_iteratorNormalCompletion4 = (_step4 = _iterator4.next()).done); _iteratorNormalCompletion4 = true) {
|
|
var state = _step4.value;
|
|
var _iteratorNormalCompletion5 = true;
|
|
var _didIteratorError5 = false;
|
|
var _iteratorError5 = undefined;
|
|
|
|
try {
|
|
for (var _iterator5 = Object.keys(handledStates)[Symbol.iterator](), _step5; !(_iteratorNormalCompletion5 = (_step5 = _iterator5.next()).done); _iteratorNormalCompletion5 = true) {
|
|
var handledState = _step5.value;
|
|
|
|
// This and some previously handled state are equivalent --
|
|
// just append this state to the same set.
|
|
if (areEquivalent(state, handledState, table, alphabet)) {
|
|
handledStates[handledState].add(state);
|
|
handledStates[state] = handledStates[handledState];
|
|
continue restSets;
|
|
}
|
|
}
|
|
// Else, this state is not equivalent to any of the
|
|
// handled states -- allocate a new set for it.
|
|
} catch (err) {
|
|
_didIteratorError5 = true;
|
|
_iteratorError5 = err;
|
|
} finally {
|
|
try {
|
|
if (!_iteratorNormalCompletion5 && _iterator5.return) {
|
|
_iterator5.return();
|
|
}
|
|
} finally {
|
|
if (_didIteratorError5) {
|
|
throw _iteratorError5;
|
|
}
|
|
}
|
|
}
|
|
|
|
handledStates[state] = new Set([state]);
|
|
}
|
|
} catch (err) {
|
|
_didIteratorError4 = true;
|
|
_iteratorError4 = err;
|
|
} finally {
|
|
try {
|
|
if (!_iteratorNormalCompletion4 && _iterator4.return) {
|
|
_iterator4.return();
|
|
}
|
|
} finally {
|
|
if (_didIteratorError4) {
|
|
throw _iteratorError4;
|
|
}
|
|
}
|
|
}
|
|
|
|
// Add these handled states to all states map.
|
|
|
|
|
|
Object.assign(newTransitionMap, handledStates);
|
|
}
|
|
|
|
// Update current transition map for the handled row.
|
|
} catch (err) {
|
|
_didIteratorError3 = true;
|
|
_iteratorError3 = err;
|
|
} finally {
|
|
try {
|
|
if (!_iteratorNormalCompletion3 && _iterator3.return) {
|
|
_iterator3.return();
|
|
}
|
|
} finally {
|
|
if (_didIteratorError3) {
|
|
throw _iteratorError3;
|
|
}
|
|
}
|
|
}
|
|
|
|
currentTransitionMap = newTransitionMap;
|
|
|
|
var newSets = new Set(Object.keys(newTransitionMap).map(function (state) {
|
|
return newTransitionMap[state];
|
|
}));
|
|
|
|
all.push([].concat(_toConsumableArray(newSets)));
|
|
|
|
// Top of the stack is the current.
|
|
current = all[all.length - 1];
|
|
|
|
// Previous set.
|
|
previous = all[all.length - 2];
|
|
};
|
|
|
|
while (!sameRow(current, previous)) {
|
|
_loop();
|
|
}
|
|
|
|
// ---------------------------------------------------------------------------
|
|
// Step 2: build minimized table from the equivalent sets.
|
|
|
|
// Remap state numbers from sets to index-based.
|
|
var remaped = new Map();
|
|
var idx = 1;
|
|
current.forEach(function (set) {
|
|
return remaped.set(set, idx++);
|
|
});
|
|
|
|
// Build the minimized table from the calculated equivalent sets.
|
|
var minimizedTable = {};
|
|
|
|
var minimizedAcceptingStates = new Set();
|
|
|
|
var updateAcceptingStates = function updateAcceptingStates(set, idx) {
|
|
var _iteratorNormalCompletion = true;
|
|
var _didIteratorError = false;
|
|
var _iteratorError = undefined;
|
|
|
|
try {
|
|
for (var _iterator = set[Symbol.iterator](), _step; !(_iteratorNormalCompletion = (_step = _iterator.next()).done); _iteratorNormalCompletion = true) {
|
|
var state = _step.value;
|
|
|
|
if (accepting.has(state)) {
|
|
minimizedAcceptingStates.add(idx);
|
|
}
|
|
}
|
|
} catch (err) {
|
|
_didIteratorError = true;
|
|
_iteratorError = err;
|
|
} finally {
|
|
try {
|
|
if (!_iteratorNormalCompletion && _iterator.return) {
|
|
_iterator.return();
|
|
}
|
|
} finally {
|
|
if (_didIteratorError) {
|
|
throw _iteratorError;
|
|
}
|
|
}
|
|
}
|
|
};
|
|
|
|
var _iteratorNormalCompletion2 = true;
|
|
var _didIteratorError2 = false;
|
|
var _iteratorError2 = undefined;
|
|
|
|
try {
|
|
for (var _iterator2 = remaped.entries()[Symbol.iterator](), _step2; !(_iteratorNormalCompletion2 = (_step2 = _iterator2.next()).done); _iteratorNormalCompletion2 = true) {
|
|
var _ref = _step2.value;
|
|
|
|
var _ref2 = _slicedToArray(_ref, 2);
|
|
|
|
var set = _ref2[0];
|
|
var _idx = _ref2[1];
|
|
|
|
minimizedTable[_idx] = {};
|
|
var _iteratorNormalCompletion6 = true;
|
|
var _didIteratorError6 = false;
|
|
var _iteratorError6 = undefined;
|
|
|
|
try {
|
|
for (var _iterator6 = alphabet[Symbol.iterator](), _step6; !(_iteratorNormalCompletion6 = (_step6 = _iterator6.next()).done); _iteratorNormalCompletion6 = true) {
|
|
var symbol = _step6.value;
|
|
|
|
updateAcceptingStates(set, _idx);
|
|
|
|
// Determine original transition for this symbol from the set.
|
|
var originalTransition = void 0;
|
|
var _iteratorNormalCompletion7 = true;
|
|
var _didIteratorError7 = false;
|
|
var _iteratorError7 = undefined;
|
|
|
|
try {
|
|
for (var _iterator7 = set[Symbol.iterator](), _step7; !(_iteratorNormalCompletion7 = (_step7 = _iterator7.next()).done); _iteratorNormalCompletion7 = true) {
|
|
var originalState = _step7.value;
|
|
|
|
originalTransition = table[originalState][symbol];
|
|
if (originalTransition) {
|
|
break;
|
|
}
|
|
}
|
|
} catch (err) {
|
|
_didIteratorError7 = true;
|
|
_iteratorError7 = err;
|
|
} finally {
|
|
try {
|
|
if (!_iteratorNormalCompletion7 && _iterator7.return) {
|
|
_iterator7.return();
|
|
}
|
|
} finally {
|
|
if (_didIteratorError7) {
|
|
throw _iteratorError7;
|
|
}
|
|
}
|
|
}
|
|
|
|
if (originalTransition) {
|
|
minimizedTable[_idx][symbol] = remaped.get(currentTransitionMap[originalTransition]);
|
|
}
|
|
}
|
|
} catch (err) {
|
|
_didIteratorError6 = true;
|
|
_iteratorError6 = err;
|
|
} finally {
|
|
try {
|
|
if (!_iteratorNormalCompletion6 && _iterator6.return) {
|
|
_iterator6.return();
|
|
}
|
|
} finally {
|
|
if (_didIteratorError6) {
|
|
throw _iteratorError6;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// Update the table, and accepting states on the original DFA.
|
|
} catch (err) {
|
|
_didIteratorError2 = true;
|
|
_iteratorError2 = err;
|
|
} finally {
|
|
try {
|
|
if (!_iteratorNormalCompletion2 && _iterator2.return) {
|
|
_iterator2.return();
|
|
}
|
|
} finally {
|
|
if (_didIteratorError2) {
|
|
throw _iteratorError2;
|
|
}
|
|
}
|
|
}
|
|
|
|
dfa.setTransitionTable(minimizedTable);
|
|
dfa.setAcceptingStateNumbers(minimizedAcceptingStates);
|
|
|
|
return dfa;
|
|
}
|
|
|
|
function sameRow(r1, r2) {
|
|
if (!r2) {
|
|
return false;
|
|
}
|
|
|
|
if (r1.length !== r2.length) {
|
|
return false;
|
|
}
|
|
|
|
for (var i = 0; i < r1.length; i++) {
|
|
var s1 = r1[i];
|
|
var s2 = r2[i];
|
|
|
|
if (s1.size !== s2.size) {
|
|
return false;
|
|
}
|
|
|
|
if ([].concat(_toConsumableArray(s1)).sort().join(',') !== [].concat(_toConsumableArray(s2)).sort().join(',')) {
|
|
return false;
|
|
}
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
/**
|
|
* Checks whether two states are N-equivalent, i.e. whether they go
|
|
* to the same set on a symbol.
|
|
*/
|
|
function areEquivalent(s1, s2, table, alphabet) {
|
|
var _iteratorNormalCompletion8 = true;
|
|
var _didIteratorError8 = false;
|
|
var _iteratorError8 = undefined;
|
|
|
|
try {
|
|
for (var _iterator8 = alphabet[Symbol.iterator](), _step8; !(_iteratorNormalCompletion8 = (_step8 = _iterator8.next()).done); _iteratorNormalCompletion8 = true) {
|
|
var symbol = _step8.value;
|
|
|
|
if (!goToSameSet(s1, s2, table, symbol)) {
|
|
return false;
|
|
}
|
|
}
|
|
} catch (err) {
|
|
_didIteratorError8 = true;
|
|
_iteratorError8 = err;
|
|
} finally {
|
|
try {
|
|
if (!_iteratorNormalCompletion8 && _iterator8.return) {
|
|
_iterator8.return();
|
|
}
|
|
} finally {
|
|
if (_didIteratorError8) {
|
|
throw _iteratorError8;
|
|
}
|
|
}
|
|
}
|
|
|
|
return true;
|
|
}
|
|
|
|
/**
|
|
* Checks whether states go to the same set.
|
|
*/
|
|
function goToSameSet(s1, s2, table, symbol) {
|
|
if (!currentTransitionMap[s1] || !currentTransitionMap[s2]) {
|
|
return false;
|
|
}
|
|
|
|
var originalTransitionS1 = table[s1][symbol];
|
|
var originalTransitionS2 = table[s2][symbol];
|
|
|
|
// If no actual transition on this symbol, treat it as positive.
|
|
if (!originalTransitionS1 && !originalTransitionS2) {
|
|
return true;
|
|
}
|
|
|
|
// Otherwise, check if they are in the same sets.
|
|
return currentTransitionMap[s1].has(originalTransitionS1) && currentTransitionMap[s2].has(originalTransitionS2);
|
|
}
|
|
|
|
module.exports = {
|
|
minimize: minimize
|
|
}; |