Java实现NFA转DFA并运行

实现NFA转DFA并运行需要以下步骤：

1. 定义NFA
首先需要定义一个NFA，包括状态集合、起始状态、接受状态、转移函数等。

2. 将NFA转换为DFA
NFA的转换可以使用子集构造法，将NFA中的状态集合转换为DFA中的状态集合，同时计算每个DFA状态的转移函数。

3. 运行DFA
在转换为DFA后，可以使用DFA对输入字符串进行识别。从起始状态开始，按照输入字符串中的字符依次进行转移，当到达一个接受状态时，判断输入字符串是否被识别。

下面是一个简单的Java代码实现NFA转DFA并运行的示例：

import java.util.*;

public class NfaToDfa {
    private Set<State> nfaStates; // NFA状态集合
    private Set<State> dfaStates; // DFA状态集合
    private Map<State, Map<Character, Set<State>>> nfaTransitions; // NFA转移函数
    private Map<State, Map<Character, State>> dfaTransitions; // DFA转移函数
    private State nfaStartState; // NFA起始状态
    private Set<State> nfaAcceptStates; // NFA接受状态集合
    private State dfaStartState; // DFA起始状态
    private Set<State> dfaAcceptStates; // DFA接受状态集合

    public NfaToDfa(Set<State> nfaStates, Map<State, Map<Character, Set<State>>> nfaTransitions, State nfaStartState, Set<State> nfaAcceptStates) {
        this.nfaStates = nfaStates;
        this.nfaTransitions = nfaTransitions;
        this.nfaStartState = nfaStartState;
        this.nfaAcceptStates = nfaAcceptStates;
        this.dfaStates = new HashSet<>();
        this.dfaTransitions = new HashMap<>();
        this.dfaStartState = null;
        this.dfaAcceptStates = new HashSet<>();
    }

    public void convert() {
        // 计算NFA的ε-闭包
        Map<State, Set<State>> epsilonClosure = new HashMap<>();
        for (State state : nfaStates) {
            epsilonClosure.put(state, epsilonClosure(state));
        }

        // 子集构造法，计算DFA状态集合和转移函数
        Set<State> startStates = epsilonClosure(nfaStartState);
        dfaStartState = new State(startStates);
        dfaStates.add(dfaStartState);
        Queue<State> queue = new LinkedList<>();
        queue.offer(dfaStartState);
        while (!queue.isEmpty()) {
            State dfaState = queue.poll();
            for (char c = 'a'; c <= 'z'; c++) {
                Set<State> nfaStates = new HashSet<>();
                for (State state : dfaState.states) {
                    if (nfaTransitions.containsKey(state) && nfaTransitions.get(state).containsKey(c)) {
                        nfaStates.addAll(nfaTransitions.get(state).get(c));
                    }
                }
                Set<State> closure = new HashSet<>();
                for (State state : nfaStates) {
                    closure.addAll(epsilonClosure.get(state));
                }
                if (!closure.isEmpty()) {
                    State newState = new State(closure);
                    dfaTransitions.computeIfAbsent(dfaState, k -> new HashMap<>()).put(c, newState);
                    if (!dfaStates.contains(newState)) {
                        dfaStates.add(newState);
                        queue.offer(newState);
                    }
                }
            }
        }

        // 计算DFA的接受状态集合
        for (State dfaState : dfaStates) {
            for (State nfaState : dfaState.states) {
                if (nfaAcceptStates.contains(nfaState)) {
                    dfaAcceptStates.add(dfaState);
                    break;
                }
            }
        }
    }

    public boolean accept(String input) {
        State currentState = dfaStartState;
        for (char c : input.toCharArray()) {
            currentState = dfaTransitions.get(currentState).get(c);
            if (currentState == null) {
                return false;
            }
        }
        return dfaAcceptStates.contains(currentState);
    }

    private Set<State> epsilonClosure(State state) {
        Set<State> closure = new HashSet<>();
        Stack<State> stack = new Stack<>();
        stack.push(state);
        while (!stack.isEmpty()) {
            State s = stack.pop();
            closure.add(s);
            if (nfaTransitions.containsKey(s) && nfaTransitions.get(s).containsKey(null)) {
                for (State t : nfaTransitions.get(s).get(null)) {
                    if (!closure.contains(t)) {
                        stack.push(t);
                    }
                }
            }
        }
        return closure;
    }

    private static class State {
        private Set<State> states;

        public State(Set<State> states) {
            this.states = states;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            State state = (State) o;
            return Objects.equals(states, state.states);
        }

        @Override
        public int hashCode() {
            return Objects.hash(states);
        }
    }
}

使用示例：

Set<NfaToDfa.State> nfaStates = new HashSet<>();
NfaToDfa.State nfaStartState = new NfaToDfa.State(Collections.singleton(nfaState1));
Set<NfaToDfa.State> nfaAcceptStates = Collections.singleton(nfaState4);
Map<NfaToDfa.State, Map<Character, Set<NfaToDfa.State>>> nfaTransitions = new HashMap<>();
nfaTransitions.put(nfaState1, Collections.singletonMap('a', Collections.singleton(nfaState2)));
nfaTransitions.put(nfaState2, Collections.singletonMap(null, Collections.singleton(nfaState3)));
nfaTransitions.put(nfaState3, Collections.singletonMap('b', Collections.singleton(nfaState4)));
NfaToDfa nfaToDfa = new NfaToDfa(nfaStates, nfaTransitions, nfaStartState, nfaAcceptStates);
nfaToDfa.convert();
System.out.println(nfaToDfa.accept("ab")); // true
System.out.println(nfaToDfa.accept("abc")); // false