[英]constructing CFG
How can I construct a Context-Free Grammer for the language x^ay^bz^2(a+b) where a>=0, b>=0. 如何为语言x ^ ay ^ bz ^ 2(a + b)构造一个上下文无关的Grammer,其中a> = 0,b> = 0。 Thanks for helps...
感谢您的帮助...
Think of it this way 这样想吧
x^a y^b z^2(a+b) = x^a y^b z^2a z^2b = x^a y^b (z^2)^b (z^2)^a
Therefore 因此
S -> xSzz | S1
S1 -> yS1zz | e
Observe that for each x
and for each y
, you need to generate two z
's because of the 2( a + b ). 观察到每个
x
和每个y
,由于2( a + b ),需要生成两个z
。 Also, observe that each string can be viewed as an "inside" part of y
's and z
's, and an "outside" part of x
's and z
's. 另外,观察到每个字符串能够作为一个“内部”部分被看作
y
的和z
的,和的‘外’部x
的和z
的。
Since for each y
you need two z
's, the inside part can be described by (using capitals to denote non-terminal symbols and []
for the empty string): 由于每个
y
需要两个z
,因此内部部分可以用(用大写字母表示非终结符,用[]
表示空字符串)来描述:
I --> []
I --> y I z z
Now write a grammar for the outside part in the same way, but referring to I
in the base case. 现在以相同的方式为外部编写语法,但在基本情况下引用
I
There are essentially two cases that you need to treat: 您实际上需要处理两种情况:
x
at the beginning of the string, in which case you need to add two z
's at the end. x
,在这种情况下,您需要在字符串的末尾添加两个z
。 y
in the middle, in which case you also need to add two z
's at the end. y
,在这种情况下,您还需要在末尾添加两个z
。 Try reducing either of these descriptions to a simpler grammer (eg a^nb^n
) for which you know the solution. 尝试将这些描述中的任何一个简化为您知道解决方案的简单语法(例如
a^nb^n
)。
This hint should be enough to deduce the generative grammer. 这个提示应该足以推断出生成的语法。
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