[英]Intersection of two DFA, how many states? Final States?
Consider the following languages over = {0, 1}, 在= {0,1}中考虑以下语言,
A = {2 : w contains 011 as a substring} B = the language matched by the regular expression 0(0 + 1)*1 A = {2:w包含011作为子字符串} B =与正则表达式0(0 + 1)* 1匹配的语言
Let M(B) be the DFA obtained by converting N(B) using the subset construction with all unnecessary states removed. 令M(B)为通过使用子集结构转换N(B)并去除所有不必要状态而获得的DFA。 Let ¬M(B) be the DFA obtained by swapping the final and non-final states of MB. 令¬M(B)为通过交换MB的最终状态和非最终状态而获得的DFA。 Let M be the product of M(A) and ¬M(B) with all unnecessary state removed. 令M为M(A)和¬M(B)的乘积,并删除所有不必要的状态。
How many states would M have? M将拥有几个州? How many final states would M have? M将拥有几个最终状态? How many states does M(B) have? M(B)有多少个状态? This question has been boggling me, I have spent a few hours on jFlap putting together the intersection of these two DFA, for A and ¬B. 这个问题一直困扰着我,我在jFlap上花了几个小时,将这两个DFA的交集放在一起,用于A和¬B。 No success. 没有成功 Thank you. 谢谢。
The language M has to satisfy 2 conditions, 语言M必须满足2个条件,
1) M(A) - has to have a substring 011
1)M(A)-必须具有子字符串011
2) ¬M(B) - should not start with 0
and end with 1
2)¬M(B)-不应以0
开头并以1
结束
You can solve this by breaking the language M into 2 parts, 您可以通过将语言M分为两部分来解决此问题,
1) that starts with 0
but does not end with 1
and having substring 001
1)以0
开头但不以1
结尾并且具有子字符串001
2) and another that starts with 1
and having substring 001
2)和另一个以1
开头并具有子字符串001
字符串
Therefore the DFA for M would be something like this 因此,M的DFA将是这样的
The states from 2-5 takes care of part 1, and states from 6-9 takes care of part 2 2-5的状态负责第1部分,而6-9的状态负责第2部分
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