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Question

这个任务我遇到了很多问题：

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...

但这不是最佳解决方案，因为你还必须改变S的位置，它会产生太多的情况。此外，它只是一个列举的案例，而不是一个“一般解决方案”，显然不是目标。

Answer 1

我建议引入辅助非终端符号：

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

然后语法可以表达如下：

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