用Java实现DFA的最小化

好的，以下是一个简单的Java代码示例来实现DFA的最小化：

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。