[英]Constructing a CFG
I literally can't find the answer to this: 我从字面上找不到答案:
L = {vw | L = {vw | v element of {a,b) , w element of {b,c} , number of a's <= number of c's}
{a,b)的v元素,{ b,c}的w元素,a的数量<= c的数量}
V --> aV | V-> aV | bV |
bV | e
Ë
W --> bW | W-> bW | cW |
连续 e
Ë
But I cannot think of how to combine the construction of the words v and w after one another and keeping in mind the mentioned restriction.. Anyone who could lend me a hand? 但是我想不出如何将v和w两个词的构造相互结合起来,并牢记上述限制。任何人都可以伸出援手吗?
As I explained in my answers tips for writing cfg , correct approach is first understand all possible patterns of strings in language then write rules. 正如我在回答cfg的提示中所解释的那样,正确的方法是首先理解语言中所有可能的字符串模式,然后编写规则。
What is this language L?
L是什么语言? In strings of language L:
使用语言L的字符串:
1. All 'a'
s comes before any 'c'
s 1.所有
'a'
都在任何'c'
之前
2. Number of 'a'
are less than or equals to number of 'c'
, So in grammar of L, if a production rule adds one symbol 'a'
then it must also add one or more 'c'
. 2.数
'a'
小于或等于的数'c'
,所以在升语法,如果产生式规则增加了一个符号'a'
那么它也必须添加一个或多个'c'
。
3. There is no restriction on occurrence of symbol 'b'
, it can appear anywhere any number of times. 3.符号
'b'
出现没有限制,它可以出现在任意位置多次。 4. Empty (null) string is also belongs to L as number of 'a'
= number if 'c'
== 0. And for same reason a string consists of only symbol 'b'
is also acceptable. 4.空(空)字符串也属于L,因为
'a'
=数字(如果'c'
== 0)。出于同样的原因,字符串仅包含符号'b'
也是可以接受的。
5. Any string without 'a'
also belongs L (in other words (c + b)*
is subset of L). 5.任何没有
'a'
字符串也属于L(换句话说(c + b)*
是L的子集)。
Now writing grammar rules are easy (read comments to understand each production rules): 现在编写语法规则很容易(阅读注释以了解每个生产规则):
S → BaBSBCB | ^ // add `a` add `C` also, B can be any where so added B
Z → CZ | BZ | ^ // to create `(c + b)*`
C → cC | c // C always generates one or more `c`s
B → bB | ^ // there is no restriction on B it generates `b`s or ^
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