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Question

我在執行此任務時遇到了一個問題：

L = {w element of {a,b}* | 
       the number of a's plus 2 times the number of b's modulo 5 in w is 0}

我想到了：

S -> ε

S -> abbS

S -> babS

S -> bbaS

S -> aaaaaS

S -> aaabS

等等...

但這不是最佳解決方案，因為您還必須移動S的位置，否則會產生太多情況。 同樣，這僅僅是對案件的列舉，而不是“一般解決方案”，這顯然不是目標。

Answer 1

我建議介紹輔助的非終端符號：

• M5 = a the number of a's plus 2 times the number of b's modulo 5 in w is 0
• M4 = a the number of a's plus 2 times the number of b's modulo 4 in w is 0
• M3 = a the number of a's plus 2 times the number of b's modulo 3 in w is 0
• M2 = a the number of a's plus 2 times the number of b's modulo 2 in w is 0

然后，語法可以表示如下：

S -> ε
S -> M5 S

M5 -> a M4
M5 -> M4 a
M5 -> b M3
M5 -> M3 b

M4 -> a M3
M4 -> M3 a
M4 -> b M2
M4 -> M2 b

M3 -> a M2
M3 -> M2 a
M3 -> b a
M3 -> a b

M2 -> a a
M2 -> b