运用Java代码和dfaRecognize函数实现E' → E → E + T → E + F → E + id → id * id + id

首先，我们需要定义一个 DFA（Deterministic Finite Automaton）来识别该文法。下面是 DFA 的状态转移图：

              +-----------+
              |           |
              |   start   |
              |           |
              +-----+-----+
                    |
                    |
                    v
              +-----+-----+
              |           |
              |     E     |
              |           |
              +-----+-----+
                    |
                    |
        +-----------+-----------+
        |                       |
        v                       v
  +-----+-----+           +-----+-----+
  |           |           |           |
  |     T     |           |     F     |
  |           |           |           |
  +-----+-----+           +-----+-----+
        |                       |
        |                       |
        v                       v
  +-----+-----+           +-----+-----+
  |           |           |           |
  |     id    |           |     id    |
  |           |           |           |
  +-----------+           +-----------+
        |                       |
        |                       |
        v                       v
  +-----+-----+           +-----+-----+
  |           |           |           |
  |     +     |           |     *     |
  |           |           |           |
  +-----------+           +-----------+
        |                       |
        |                       |
        v                       v
  +-----+-----+           +-----+-----+
  |           |           |           |
  |     E     |           |     id    |
  |           |           |           |
  +-----------+           +-----------+

其中，状态 E、T、F 分别表示对应的非终结符，状态 id、+、* 表示对应的终结符。

根据 DFA 的状态转移图，我们可以用 Java 代码实现一个 DFA 识别器。下面是示例代码：

public class DfaRecognize {
    private static final int STATE_START = 0;
    private static final int STATE_E = 1;
    private static final int STATE_T = 2;
    private static final int STATE_F = 3;
    private static final int STATE_ID = 4;
    private static final int STATE_PLUS = 5;
    private static final int STATE_MULTIPLY = 6;

    private static final int[] FINAL_STATES = {STATE_ID, STATE_PLUS, STATE_MULTIPLY};

    private static final int[][] TRANS_TABLE = {
            //         id   +    *   (other)
            /* start */{STATE_ID, -1, -1, STATE_E},
            /* E     */{STATE_T, STATE_PLUS, -1, -1},
            /* T     */{STATE_F, -1, STATE_MULTIPLY, -1},
            /* F     */{STATE_ID, -1, -1, -1},
            /* id    */{-1, -1, -1, -1},
            /* +     */{-1, -1, -1, STATE_E},
            /* *     */{STATE_ID, -1, -1, -1},
    };

    public static boolean recognize(String input) {
        int state = STATE_START;
        for (char ch : input.toCharArray()) {
            int inputType;
            if (ch == 'id') {
                inputType = 0;
            } else if (ch == '+') {
                inputType = 1;
            } else if (ch == '*') {
                inputType = 2;
            } else {
                inputType = 3;
            }

            state = TRANS_TABLE[state][inputType];
            if (state == -1) {
                return false;
            }
        }

        for (int finalState : FINAL_STATES) {
            if (state == finalState) {
                return true;
            }
        }

        return false;
    }
}

最后，我们可以使用 DFA 识别器来判断一个字符串是否符合该文法：

String input = "id * id + id";
if (DfaRecognize.recognize(input)) {
    System.out.println("符合文法");
} else {
    System.out.println("不符合文法");
}