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using Implab;
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using System;
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using System.Collections.Generic;
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using System.Linq;
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namespace Implab.Automaton {
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public class DFADefinition<TInput, TState, TTag> : IDFADefinitionBuilder<TTag>, IDFADefinition<TInput, TState, TTag> {
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DFAStateDescriptior<TTag>[] m_dfaTable;
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readonly IAlphabet<TInput> m_inputAlphabet;
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readonly IAlphabet<TState> m_stateAlphabet;
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readonly Dictionary<int, TTag[]> m_finalStates = new Dictionary<int, TTag[]>();
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readonly HashSet<AutomatonTransition> m_transitions = new HashSet<AutomatonTransition>();
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public DFADefinition(IAlphabet<TInput> inputAlphabet, IAlphabet<TState> stateAlphabet) {
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Safe.ArgumentNotNull(inputAlphabet, "inputAlphabet");
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Safe.ArgumentNotNull(stateAlphabet, "stateAlphabet");
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m_inputAlphabet = inputAlphabet;
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m_stateAlphabet = stateAlphabet;
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}
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public void DefineTransition(int s1, int s2, int symbol) {
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Safe.ArgumentInRange(s1, 0, m_stateAlphabet.Count-1, "s1");
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Safe.ArgumentInRange(s2, 0, m_stateAlphabet.Count-1, "s2");
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Safe.ArgumentInRange(symbol, 0, m_inputAlphabet.Count-1, "symbol");
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m_transitions.Add(new AutomatonTransition(s1, s2, symbol));
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}
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#region IDFADefinition implementation
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public DFAStateDescriptior<TTag>[] GetTransitionTable() {
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if (m_dfaTable == null) {
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m_dfaTable = new DFAStateDescriptior<TTag>[m_stateAlphabet.Count];
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foreach (var pair in m_finalStates) {
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var idx = pair.Key;
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m_dfaTable[idx].final = true;
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m_dfaTable[idx].tag = m_dfaTable[idx].tag != null ?
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m_dfaTable[idx].tag.Concat(pair.Value).Distinct().ToArray() :
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pair.Value;
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}
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foreach (var t in m_transitions) {
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if (m_dfaTable[t.s1].transitions == null) {
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m_dfaTable[t.s1].transitions = new int[m_inputAlphabet.Count];
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for (int i = 0; i < m_dfaTable[t.s1].transitions.Length; i++)
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m_dfaTable[t.s1].transitions[i] = DFAConst.UNREACHABLE_STATE;
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}
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m_dfaTable[t.s1].transitions[t.edge] = t.s2;
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}
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}
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return m_dfaTable;
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}
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public IAlphabet<TInput> InputAlphabet {
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get {
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return m_inputAlphabet;
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}
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}
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public IAlphabet<TState> StateAlphabet {
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get {
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return m_stateAlphabet;
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}
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}
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#endregion
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#region IDFADefinitionBuilder
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public void DefineTransition(int s1, int s2, int symbol) {
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Safe.ArgumentInRange(s1, 0, m_stateAlphabet.Count - 1, "s1");
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Safe.ArgumentInRange(s2, 0, m_stateAlphabet.Count - 1, "s2");
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Safe.ArgumentInRange(symbol, 0, m_inputAlphabet.Count - 1, "symbol");
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m_transitions.Add(new AutomatonTransition(s1, s2, symbol));
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}
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public void MarkFinalState(int state, params TTag[] tags) {
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m_finalStates[state] = tags;
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}
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#endregion
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protected void Optimize(IDFADefinitionBuilder<TTag> optimalDFA,IAlphabetBuilder<TInput> optimalInputAlphabet, IAlphabetBuilder<TState> optimalStateAlphabet) {
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Safe.ArgumentNotNull(optimalDFA, "dfa");
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Safe.ArgumentNotNull(optimalInputAlphabet, "optimalInputAlphabet");
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Safe.ArgumentNotNull(optimalStateAlphabet, "optimalStateAlphabet");
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var setComparer = new CustomEqualityComparer<HashSet<int>>(
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(x, y) => x.SetEquals(y),
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s => s.Sum(x => x.GetHashCode())
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);
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var arrayComparer = new CustomEqualityComparer<TTag[]>(
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(x,y) => (new HashSet<int>(x)).SetEquals(new HashSet<int>(y)),
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a => a.Sum(x => x.GetHashCode())
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);
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var optimalStates = new HashSet<HashSet<int>>(setComparer);
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var queue = new HashSet<HashSet<int>>(setComparer);
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// получаем конечные состояния, сгруппированные по маркерам
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optimalStates.UnionWith(
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m_finalStates
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.GroupBy(pair => pair.Value, arrayComparer)
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.Select(
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g => new HashSet<int>(
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g.Select( pair => pair.Key)
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)
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)
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);
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var state = new HashSet<int>(
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Enumerable
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.Range(0, m_stateAlphabet.Count - 1)
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.Where(i => !m_finalStates.ContainsKey(i))
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);
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optimalStates.Add(state);
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queue.Add(state);
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var rmap = m_transitions
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.GroupBy(t => t.s2)
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.ToLookup(
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g => g.Key, // s2
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g => g.ToLookup(t => t.edge, t => t.s1)
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);
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while (queue.Count > 0) {
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var stateA = queue.First();
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queue.Remove(stateA);
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for (int c = 0; c < m_inputAlphabet.Count; c++) {
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var stateX = new HashSet<int>();
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foreach(var a in stateA)
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stateX.UnionWith(rmap[a][c]); // all states from wich 'c' leads to 'a'
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foreach (var stateY in optimalStates.ToArray()) {
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if (stateX.Overlaps(stateY) && !stateY.IsSubsetOf(stateX)) {
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var stateR1 = new HashSet<int>(stateY);
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var stateR2 = new HashSet<int>(stateY);
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stateR1.IntersectWith(stateX);
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stateR2.ExceptWith(stateX);
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optimalStates.Remove(stateY);
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optimalStates.Add(stateR1);
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optimalStates.Add(stateR2);
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if (queue.Contains(stateY)) {
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queue.Remove(stateY);
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queue.Add(stateR1);
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queue.Add(stateR2);
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} else {
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queue.Add(stateR1.Count <= stateR2.Count ? stateR1 : stateR2);
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}
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}
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}
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}
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}
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// карта получения оптимального состояния по соотвествующему ему простому состоянию
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var statesMap = m_stateAlphabet.Reclassify(optimalStateAlphabet, optimalStates);
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// получаем минимальный алфавит
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// входные символы не различимы, если Move(s,a1) == Move(s,a2)
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var optimalAlphabet = m_transitions
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.GroupBy(t => Tuple.Create(statesMap[t.s1], statesMap[t.s2]), t => t.edge);
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var alphabetMap = m_inputAlphabet.Reclassify(optimalInputAlphabet, optimalAlphabet);
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var optimalTags = m_finalStates
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.GroupBy(pair => statesMap[pair.Key])
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.ToDictionary(
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g => g.Key,
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g => g.SelectMany(pair => pair.Value).ToArray()
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);
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// построение автомата
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foreach (var pair in optimalTags)
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optimalDFA.MarkFinalState(pair.Key, pair.Value);
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foreach (var t in m_transitions.Select(t => new AutomatonTransition(statesMap[t.s1],statesMap[t.s2],alphabetMap[t.edge])).Distinct())
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optimalDFA.DefineTransition(t.s1, t.s2, t.edge);
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}
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public void PrintDFA() {
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var inputMap = InputAlphabet.CreateReverseMap();
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var stateMap = StateAlphabet.CreateReverseMap();
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for (int i = 0; i < inputMap.Length; i++) {
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Console.WriteLine("C{0}: {1}", i, String.Join(",", inputMap[i]));
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}
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foreach(var t in m_transitions)
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Console.WriteLine(
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"S{0} -{1}-> S{2}{3}",
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stateMap[t.s1],
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String.Join(",", inputMap[t.edge]),
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stateMap[t.s2],
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m_finalStates.ContainsKey(t.s2) ? "$" : ""
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);
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}
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}
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}
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