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1 | using Implab; | |
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2 | using System; | |
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3 | using System.Collections.Generic; | |
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4 | using System.Linq; | |
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5 | ||
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6 | namespace Implab.Automaton { | |
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7 | public class DFATable : IDFATableBuilder { | |
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8 | DFAStateDescriptior[] m_dfaTable; | |
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9 | ||
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10 | int m_stateCount; | |
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11 | int m_symbolCount; | |
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12 | int m_initialState; | |
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13 | ||
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14 | readonly HashSet<int> m_finalStates = new HashSet<int>(); | |
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15 | readonly HashSet<AutomatonTransition> m_transitions = new HashSet<AutomatonTransition>(); | |
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16 | ||
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17 | void AssertNotReadOnly() { | |
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18 | if (m_dfaTable != null) | |
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19 | throw new InvalidOperationException("The object is readonly"); | |
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20 | } | |
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21 | ||
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22 | ||
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23 | #region IDFADefinition implementation | |
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24 | ||
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25 | public DFAStateDescriptior[] GetTransitionTable() { | |
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26 | if (m_dfaTable == null) { | |
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27 | if (m_stateCount <= 0) | |
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28 | throw new InvalidOperationException("Invalid automaton definition: states count = {0}", m_stateCount); | |
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29 | if (m_symbolCount <= 0) | |
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30 | throw new InvalidOperationException("Invalid automaton definition: symbols count = {0}", m_symbolCount); | |
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31 | ||
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32 | m_dfaTable = ConstructTransitionTable(); | |
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33 | } | |
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34 | return m_dfaTable; | |
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35 | } | |
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36 | ||
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37 | public bool IsFinalState(int s) { | |
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38 | Safe.ArgumentInRange(s, 0, m_stateCount, "s"); | |
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39 | ||
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40 | return m_dfaTable != null ? m_dfaTable[s].final : m_finalStates.Contains(s); | |
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41 | } | |
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42 | ||
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43 | public IEnumerable<int> FinalStates { | |
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44 | get { | |
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45 | return m_finalStates; | |
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46 | } | |
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47 | } | |
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48 | ||
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49 | public int StateCount { | |
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50 | get { return m_stateCount; } | |
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51 | } | |
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52 | ||
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53 | public int AlphabetSize { | |
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54 | get { return m_symbolCount; } | |
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55 | } | |
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56 | ||
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57 | public int InitialState { | |
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58 | get { return m_initialState; } | |
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59 | } | |
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60 | ||
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61 | #endregion | |
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62 | ||
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63 | protected virtual DFAStateDescriptior[] ConstructTransitionTable() { | |
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64 | var dfaTable = new DFAStateDescriptior[m_stateCount]; | |
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65 | ||
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66 | ||
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67 | foreach (var t in m_transitions) { | |
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68 | if (dfaTable[t.s1].transitions == null) | |
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69 | dfaTable[t.s1] = new DFAStateDescriptior(m_symbolCount, m_finalStates.Contains(t.s1)); | |
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70 | ||
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71 | dfaTable[t.s1].transitions[t.edge] = t.s2; | |
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72 | } | |
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73 | ||
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74 | foreach (var s in m_finalStates) | |
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75 | if (!dfaTable[s].final) | |
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76 | m_dfaTable[s] = new DFAStateDescriptior(m_symbolCount, true); | |
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77 | ||
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78 | } | |
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79 | ||
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80 | public void SetInitialState(int s) { | |
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81 | Safe.ArgumentAssert(s >= 0, "s"); | |
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82 | m_initialState = s; | |
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83 | } | |
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84 | ||
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85 | public void MarkFinalState(int state) { | |
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86 | AssertNotReadOnly(); | |
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87 | m_finalStates.Add(state); | |
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88 | } | |
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89 | ||
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90 | public void Add(AutomatonTransition item) { | |
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91 | AssertNotReadOnly(); | |
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92 | Safe.ArgumentAssert(item.s1 >= 0, "item"); | |
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93 | Safe.ArgumentAssert(item.s2 >= 0, "item"); | |
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94 | Safe.ArgumentAssert(item.edge >= 0, "item"); | |
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95 | ||
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96 | m_stateCount = Math.Max(m_stateCount, Math.Max(item.s1, item.s2) + 1); | |
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97 | m_symbolCount = Math.Max(m_symbolCount, item.edge); | |
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98 | ||
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99 | m_transitions.Add(item); | |
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100 | } | |
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101 | ||
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102 | public void Clear() { | |
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103 | AssertNotReadOnly(); | |
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104 | ||
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105 | m_stateCount = 0; | |
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106 | m_symbolCount = 0; | |
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107 | m_finalStates.Clear(); | |
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108 | m_transitions.Clear(); | |
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109 | } | |
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110 | ||
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111 | public bool Contains(AutomatonTransition item) { | |
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112 | return m_transitions.Contains(item); | |
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113 | } | |
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114 | ||
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115 | public void CopyTo(AutomatonTransition[] array, int arrayIndex) { | |
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116 | m_transitions.CopyTo(array, arrayIndex); | |
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117 | } | |
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118 | ||
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119 | public bool Remove(AutomatonTransition item) { | |
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120 | AssertNotReadOnly(); | |
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121 | m_transitions.Remove(item); | |
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122 | } | |
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123 | ||
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124 | public int Count { | |
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125 | get { | |
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126 | return m_transitions.Count; | |
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127 | } | |
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128 | } | |
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129 | ||
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130 | public bool IsReadOnly { | |
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131 | get { | |
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132 | return m_dfaTable != null; | |
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133 | } | |
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134 | } | |
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135 | ||
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136 | public IEnumerator<AutomatonTransition> GetEnumerator() { | |
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137 | return m_transitions.GetEnumerator(); | |
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138 | } | |
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139 | ||
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140 | System.Collections.IEnumerator System.Collections.IEnumerable.GetEnumerator() { | |
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141 | return GetEnumerator(); | |
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142 | } | |
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143 | ||
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144 | /// <summary>Формирует множества конечных состояний перед началом работы алгоритма минимизации.</summary> | |
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145 | /// <remarks> | |
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146 | /// В процессе построения минимального автомата требуется разделить множество состояний, | |
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147 | /// на два подмножества - конечные состояния и все остальные, после чего эти подмножества | |
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148 | /// будут резделены на более мелкие. Иногда требуется гарантировать различия конечных сосотяний, | |
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149 | /// для этого необходимо переопределить даннцю фукнцию, для получения множеств конечных состояний. | |
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150 | /// </remarks> | |
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151 | /// <returns>The final states.</returns> | |
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152 | protected virtual IEnumerable<HashSet<int>> GroupFinalStates() { | |
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153 | return new HashSet<int>[] { m_finalStates }; | |
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154 | } | |
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155 | ||
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156 | protected void Optimize<TInput, TState>( | |
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157 | IDFATableBuilder optimalDFA, | |
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158 | IAlphabet<TInput> inputAlphabet, | |
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159 | IAlphabetBuilder<TInput> optimalInputAlphabet, | |
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160 | IAlphabet<TState> stateAlphabet, | |
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161 | IAlphabetBuilder<TState> optimalStateAlphabet | |
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162 | ) { | |
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163 | Safe.ArgumentNotNull(optimalDFA, "dfa"); | |
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164 | Safe.ArgumentNotNull(optimalInputAlphabet, "optimalInputAlphabet"); | |
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165 | Safe.ArgumentNotNull(optimalStateAlphabet, "optimalStateAlphabet"); | |
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166 | Safe.ArgumentNotNull(inputAlphabet, "inputAlphabet"); | |
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167 | Safe.ArgumentNotNull(stateAlphabet, "stateAlphabet"); | |
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168 | ||
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169 | if (inputAlphabet.Count != m_symbolCount) | |
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170 | throw new InvalidOperationException("The input symbols aphabet mismatch"); | |
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171 | if (stateAlphabet.Count != m_stateCount) | |
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172 | throw new InvalidOperationException("The states alphabet mismatch"); | |
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173 | ||
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174 | var setComparer = new CustomEqualityComparer<HashSet<int>>( | |
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175 | (x, y) => x.SetEquals(y), | |
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176 | s => s.Sum(x => x.GetHashCode()) | |
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177 | ); | |
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178 | ||
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179 | var optimalStates = new HashSet<HashSet<int>>(setComparer); | |
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180 | var queue = new HashSet<HashSet<int>>(setComparer); | |
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181 | ||
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182 | // получаем конечные состояния, сгруппированные по маркерам | |
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183 | optimalStates.UnionWith( | |
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184 | GroupFinalStates() | |
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185 | ); | |
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186 | ||
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187 | var state = new HashSet<int>( | |
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188 | Enumerable | |
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189 | .Range(0, m_stateCount - 1) | |
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190 | .Where(i => !m_finalStates.Contains(i)) | |
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191 | ); | |
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192 | ||
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193 | optimalStates.Add(state); | |
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194 | queue.Add(state); | |
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195 | ||
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196 | var rmap = m_transitions | |
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197 | .GroupBy(t => t.s2) | |
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198 | .ToLookup( | |
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199 | g => g.Key, // s2 | |
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200 | g => g.ToLookup(t => t.edge, t => t.s1) | |
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201 | ); | |
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202 | ||
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203 | while (queue.Count > 0) { | |
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204 | var stateA = queue.First(); | |
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205 | queue.Remove(stateA); | |
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206 | ||
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207 | for (int c = 0; c < m_symbolCount; c++) { | |
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208 | var stateX = new HashSet<int>(); | |
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209 | foreach(var a in stateA) | |
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210 | stateX.UnionWith(rmap[a][c]); // all states from wich 'c' leads to 'a' | |
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211 | ||
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212 | foreach (var stateY in optimalStates.ToArray()) { | |
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213 | if (stateX.Overlaps(stateY) && !stateY.IsSubsetOf(stateX)) { | |
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214 | var stateR1 = new HashSet<int>(stateY); | |
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215 | var stateR2 = new HashSet<int>(stateY); | |
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216 | ||
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217 | stateR1.IntersectWith(stateX); | |
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218 | stateR2.ExceptWith(stateX); | |
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219 | ||
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220 | optimalStates.Remove(stateY); | |
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221 | optimalStates.Add(stateR1); | |
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222 | optimalStates.Add(stateR2); | |
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223 | ||
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224 | if (queue.Contains(stateY)) { | |
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225 | queue.Remove(stateY); | |
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226 | queue.Add(stateR1); | |
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227 | queue.Add(stateR2); | |
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228 | } else { | |
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229 | queue.Add(stateR1.Count <= stateR2.Count ? stateR1 : stateR2); | |
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230 | } | |
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231 | } | |
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232 | } | |
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233 | } | |
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234 | } | |
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235 | ||
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236 | // карта получения оптимального состояния по соотвествующему ему простому состоянию | |
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237 | var statesMap = stateAlphabet.Reclassify(optimalStateAlphabet, optimalStates); | |
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238 | ||
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239 | // получаем минимальный алфавит | |
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240 | // входные символы не различимы, если Move(s,a1) == Move(s,a2) | |
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241 | var optimalAlphabet = m_transitions | |
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242 | .GroupBy(t => Tuple.Create(statesMap[t.s1], statesMap[t.s2]), t => t.edge); | |
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243 | ||
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244 | var alphabetMap = inputAlphabet.Reclassify(optimalInputAlphabet, optimalAlphabet); | |
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245 | ||
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246 | // построение автомата | |
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247 | optimalDFA.SetInitialState(statesMap[m_initialState]); | |
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248 | ||
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249 | foreach (var sf in m_finalStates.GroupBy(s => statesMap[s])) | |
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250 | optimalDFA.MarkFinalState(sf.Key); | |
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251 | ||
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252 | foreach (var t in m_transitions.Select(t => new AutomatonTransition(statesMap[t.s1],statesMap[t.s2],alphabetMap[t.edge])).Distinct()) | |
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253 | optimalDFA.Add(t); | |
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254 | ||
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255 | } | |
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256 | ||
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257 | protected void PrintDFA<TInput, TState>(IAlphabet<TInput> inputAlphabet, IAlphabet<TState> stateAlphabet) { | |
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258 | Safe.ArgumentNotNull(inputAlphabet, "inputAlphabet"); | |
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259 | Safe.ArgumentNotNull(stateAlphabet, "stateAlphabet"); | |
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260 | ||
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261 | var inputMap = inputAlphabet.CreateReverseMap(); | |
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262 | var stateMap = stateAlphabet.CreateReverseMap(); | |
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263 | ||
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264 | for (int i = 0; i < inputMap.Length; i++) | |
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265 | Console.WriteLine("C{0}: {1}", i, String.Join(",", inputMap[i])); | |
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266 | ||
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267 | ||
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268 | foreach(var t in m_transitions) | |
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269 | Console.WriteLine( | |
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270 | "[{0}] -{{{1}}}-> [{2}]{3}", | |
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271 | stateMap[t.s1], | |
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272 | String.Join(",", inputMap[t.edge]), | |
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273 | stateMap[t.s2], | |
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274 | m_finalStates.Contains(t.s2) ? "$" : "" | |
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275 | ); | |
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276 | ||
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277 | } | |
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278 | ||
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279 | } | |
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280 | } |
@@ -0,0 +1,9 | |||
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1 | using System; | |
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2 | ||
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3 | namespace Implab.Automaton.RegularExpressions { | |
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4 | public interface IDFATable2<TTag> : IDFATable { | |
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5 | void MarkFinalState(int state, TTag[] tags); | |
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6 | ||
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7 | } | |
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8 | } | |
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9 |
@@ -11,5 +11,16 | |||
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11 | 11 | |
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12 | 12 | public DFAStateDescriptior(int[] transitions) : this(transitions, false) { |
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13 | 13 | } |
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14 | ||
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15 | public DFAStateDescriptior(int size, bool final) { | |
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16 | Safe.ArgumentInRange(size, 0, int.MaxValue, "size"); | |
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17 | ||
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18 | this.final = final; | |
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19 | ||
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20 | transitions = new int[size]; | |
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21 | ||
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22 | for (int i = 0; i < size; i++) | |
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23 | transitions[i] = DFAConst.UNREACHABLE_STATE; | |
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14 | 24 | } |
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15 | 25 | } |
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26 | } |
@@ -1,7 +1,7 | |||
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1 | 1 | using System; |
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2 | 2 | |
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3 | 3 | namespace Implab.Automaton.RegularExpressions { |
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4 |
public class RegularDFADefinition<TInput, TTag> : DFAT |
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4 | public class RegularDFADefinition<TInput, TTag> : DFATable { | |
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5 | 5 | |
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6 | 6 | readonly IAlphabet<TInput> m_alphabet; |
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7 | 7 | |
@@ -18,7 +18,7 namespace Implab.Automaton.RegularExpres | |||
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18 | 18 | } |
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19 | 19 | } |
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20 | 20 | |
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21 |
protected override DFAStateDescriptior |
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21 | protected override DFAStateDescriptior[] ConstructTransitionTable() { | |
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22 | 22 | if (InputAlphabet.Count != m_alphabet.Count) |
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23 | 23 | throw new InvalidOperationException("The alphabet doesn't match the transition table"); |
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24 | 24 |
@@ -183,13 +183,14 | |||
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183 | 183 | <Compile Include="Formats\JSON\StringTranslator.cs" /> |
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184 | 184 | <Compile Include="Automaton\MapAlphabet.cs" /> |
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185 | 185 | <Compile Include="Automaton\DummyAlphabet.cs" /> |
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186 | <Compile Include="Automaton\DFATransitionTable.cs" /> | |
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187 | 186 | <Compile Include="Automaton\RegularExpressions\RegularDFADefinition.cs" /> |
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188 | 187 | <Compile Include="Formats\CharAlphabet.cs" /> |
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189 | 188 | <Compile Include="Formats\ByteAlphabet.cs" /> |
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190 | 189 | <Compile Include="Formats\RegularCharDFADefinition.cs" /> |
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191 | 190 | <Compile Include="Automaton\IDFATable.cs" /> |
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192 | 191 | <Compile Include="Automaton\IDFATableBuilder.cs" /> |
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192 | <Compile Include="Automaton\DFATable.cs" /> | |
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193 | <Compile Include="Automaton\RegularExpressions\IDFATable2.cs" /> | |
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193 | 194 | </ItemGroup> |
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194 | 195 | <Import Project="$(MSBuildBinPath)\Microsoft.CSharp.targets" /> |
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195 | 196 | <ItemGroup /> |
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