Java实现NFA转DFA并给出使用示例

NFA（非确定有限状态自动机）是一种能够接受正则表达式描述的语言的自动机，而DFA（确定有限状态自动机）是一种处理有限长度字符串的自动机。将NFA转换为DFA可以使得语言的识别更高效，因为DFA比NFA更容易实现。

下面是一个Java实现NFA转DFA的示例代码：

import java.util.*;

public class NFAtoDFA {
    private Set<Integer> states;
    private Set<Character> symbols;
    private int initialState;
    private Set<Integer> finalStates;
    private Map<Integer, Map<Character, Set<Integer>>> transitionFunction;

    public NFAtoDFA(Set<Integer> states, Set<Character> symbols, int initialState,
            Set<Integer> finalStates, Map<Integer, Map<Character, Set<Integer>>> transitionFunction) {
        this.states = states;
        this.symbols = symbols;
        this.initialState = initialState;
        this.finalStates = finalStates;
        this.transitionFunction = transitionFunction;
    }

    public DFA convertToDFA() {
        Map<Set<Integer>, Integer> dfaStates = new HashMap<>();
        List<Set<Integer>> dfaStateList = new ArrayList<>();
        int stateCount = 0;

        // Compute the epsilon closure of the initial state
        Set<Integer> initialClosure = epsilonClosure(initialState);

        // Add the initial state to the DFA
        dfaStates.put(initialClosure, stateCount);
        dfaStateList.add(initialClosure);
        stateCount++;

        // Initialize the transition function for the DFA
        Map<Integer, Map<Character, Integer>> dfaTransitionFunction = new HashMap<>();

        // Process each unmarked state in the list
        for (int i = 0; i < dfaStateList.size(); i++) {
            Set<Integer> dfaState = dfaStateList.get(i);

            // For each symbol in the input alphabet
            for (char symbol : symbols) {
                // Compute the transition for this symbol
                Set<Integer> transition = new HashSet<>();
                for (int state : dfaState) {
                    Map<Character, Set<Integer>> transitionsForState = transitionFunction.get(state);
                    if (transitionsForState != null) {
                        Set<Integer> statesOnSymbol = transitionsForState.get(symbol);
                        if (statesOnSymbol != null) {
                            transition.addAll(statesOnSymbol);
                        }
                    }
                }

                // Compute the epsilon closure of the resulting state
                Set<Integer> closure = epsilonClosure(transition);

                // If the resulting state is new, add it to the DFA
                if (!dfaStates.containsKey(closure)) {
                    dfaStates.put(closure, stateCount);
                    dfaStateList.add(closure);
                    stateCount++;
                }

                // Add the transition to the DFA transition function
                int sourceState = dfaStates.get(dfaState);
                int targetState = dfaStates.get(closure);
                if (!dfaTransitionFunction.containsKey(sourceState)) {
                    dfaTransitionFunction.put(sourceState, new HashMap<>());
                }
                dfaTransitionFunction.get(sourceState).put(symbol, targetState);
            }
        }

        // Compute the final states of the DFA
        Set<Integer> dfaFinalStates = new HashSet<>();
        for (Set<Integer> dfaState : dfaStateList) {
            for (int nfaState : dfaState) {
                if (finalStates.contains(nfaState)) {
                    dfaFinalStates.add(dfaStates.get(dfaState));
                    break;
                }
            }
        }

        // Create and return the DFA
        return new DFA(dfaStateList.size(), symbols, 0, dfaFinalStates, dfaTransitionFunction);
    }

    private Set<Integer> epsilonClosure(int state) {
        Set<Integer> closure = new HashSet<>();
        Stack<Integer> stack = new Stack<>();
        closure.add(state);
        stack.push(state);
        while (!stack.isEmpty()) {
            int currentState = stack.pop();
            Map<Character, Set<Integer>> transitionsForState = transitionFunction.get(currentState);
            if (transitionsForState != null) {
                Set<Integer> statesOnEpsilon = transitionsForState.get(null);
                if (statesOnEpsilon != null) {
                    for (int nextState : statesOnEpsilon) {
                        if (!closure.contains(nextState)) {
                            closure.add(nextState);
                            stack.push(nextState);
                        }
                    }
                }
            }
        }
        return closure;
    }
}

下面是一个使用示例：

import java.util.*;

public class NFAtoDFAExample {
    public static void main(String[] args) {
        // Define the input alphabet
        Set<Character> symbols = new HashSet<>();
        symbols.add('a');
        symbols.add('b');

        // Define the NFA
        Set<Integer> states = new HashSet<>(Arrays.asList(0, 1, 2, 3));
        int initialState = 0;
        Set<Integer> finalStates = new HashSet<>(Arrays.asList(3));
        Map<Integer, Map<Character, Set<Integer>>> transitionFunction = new HashMap<>();
        transitionFunction.put(0, new HashMap<>());
        transitionFunction.get(0).put('a', new HashSet<>(Arrays.asList(0, 1)));
        transitionFunction.get(0).put(null, new HashSet<>(Arrays.asList(2)));
        transitionFunction.put(1, new HashMap<>());
        transitionFunction.get(1).put('b', new HashSet<>(Arrays.asList(2)));
        transitionFunction.put(2, new HashMap<>());
        transitionFunction.get(2).put('a', new HashSet<>(Arrays.asList(3)));

        // Convert the NFA to a DFA
        NFAtoDFA nfaToDfa = new NFAtoDFA(states, symbols, initialState, finalStates, transitionFunction);
        DFA dfa = nfaToDfa.convertToDFA();

        // Test the DFA
        System.out.println(dfa.accepts("aab")); // true
        System.out.println(dfa.accepts("abb")); // false
    }
}

在这个示例中，我们定义了一个NFA，并使用该NFA创建了一个NFAtoDFA对象。我们然后使用该对象调用convertToDFA()方法，该方法返回一个DFA对象。我们最后测试了DFA对象是否接受一些字符串。