用Java实现DFA的最小化
时间: 2024-02-27 09:53:04 浏览: 104
好的,以下是一个简单的Java代码示例来实现DFA的最小化:
```java
public DFA minimizeDFA(DFA dfa) {
// Step 1: Initialize variables
List<String> states = dfa.getStates();
List<String> inputs = dfa.getInputs();
Map<String, Map<String, String>> transitions = dfa.getTransitions();
String startState = dfa.getStartState();
List<String> finalStates = dfa.getFinalStates();
// Step 2: Mark all states as non-equivalent
boolean[][] equivalence = new boolean[states.size()][states.size()];
// Mark all final states and non-final states as not equivalent
for (int i = 0; i < states.size(); i++) {
for (int j = 0; j < states.size(); j++) {
if ((finalStates.contains(states.get(i)) && !finalStates.contains(states.get(j))) ||
(!finalStates.contains(states.get(i)) && finalStates.contains(states.get(j)))) {
equivalence[i][j] = true;
}
}
}
// Step 3: Iterate until no more equivalences are found
while (true) {
boolean[][] newEquivalence = new boolean[states.size()][states.size()];
for (int i = 0; i < states.size(); i++) {
for (int j = i + 1; j < states.size(); j++) {
if (!equivalence[i][j]) {
for (String input : inputs) {
String si = transitions.get(states.get(i)).get(input);
String sj = transitions.get(states.get(j)).get(input);
int iIndex = states.indexOf(si);
int jIndex = states.indexOf(sj);
if (equivalence[iIndex][jIndex]) {
newEquivalence[i][j] = true;
break;
}
}
if (newEquivalence[i][j]) {
break;
}
}
}
}
if (Arrays.deepEquals(newEquivalence, equivalence)) {
break;
}
equivalence = newEquivalence;
}
// Step 4: Group states based on equivalence
Map<String, List<Integer>> groups = new HashMap<>();
for (int i = 0; i < states.size(); i++) {
for (int j = i + 1; j < states.size(); j++) {
if (!equivalence[i][j]) {
if (groups.containsKey(states.get(i))) {
groups.get(states.get(i)).add(j);
} else {
List<Integer> group = new ArrayList<>();
group.add(i);
group.add(j);
groups.put(states.get(i), group);
}
}
}
}
// Step 5: Create new DFA with minimized states
List<String> newStates = new ArrayList<>();
Map<String, Map<String, String>> newTransitions = new HashMap<>();
String newStartState = null;
List<String> newFinalStates = new ArrayList<>();
for (List<Integer> group : groups.values()) {
StringBuilder newState = new StringBuilder();
for (int i : group) {
newState.append(states.get(i));
}
newStates.add(newState.toString());
Map<String, String> transitionMap = new HashMap<>();
for (String input : inputs) {
String next = transitions.get(states.get(group.get(0))).get(input);
int nextIndex = states.indexOf(next);
for (int i = 1; i < group.size(); i++) {
String currentNext = transitions.get(states.get(group.get(i))).get(input);
int currentNextIndex = states.indexOf(currentNext);
if (currentNextIndex < nextIndex) {
next = currentNext;
nextIndex = currentNextIndex;
}
}
transitionMap.put(input, newStates.get(states.indexOf(next.substring(0, 1)) + next.substring(1)));
}
newTransitions.put(newState.toString(), transitionMap);
if (group.contains(states.indexOf(startState))) {
newStartState = newState.toString();
}
if (group.stream().anyMatch(finalStates::contains)) {
newFinalStates.add(newState.toString());
}
}
return new DFA(newStates, inputs, newTransitions, newStartState, newFinalStates);
}
```
请注意,这是一个简单的示例代码,具体实现可能因实际需求而异。但是,它演示了DFA最小化的基本步骤。希望这可以帮助您更好地理解DFA最小化的实现。
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