问题
L = w : (na(w) - nb(w)) mod 3 /= 0
How can I go about finding the regular expression for this language?
I understand that it means that the number of As minus the number of Bs cannot be a multiple of 3. So a - b cannot be 3,6,9,12, etc.
But I am still having trouble putting it into a regular expression. I tried first making it a DFA or NFA but I couldn't do that either.
Any help is appreciated!
回答1:
I would go about it by dividing the list of words on {a,b} into three cases:
- L1 = w : (na(w) - nb(w)) mod 3 = 1
- L2 = w : (na(w) - nb(w)) mod 3 = 2
- L3 = w : (na(w) - nb(w)) mod 3 = 3
L is then L1 U L2, and you should be able to create expressions relating L1, L2, and L3. You should then be able to eliminate things and end up with a regular expression on {a,b}.
来源：https://stackoverflow.com/questions/19214574/find-the-regular-expression-for-the-language-on-e-a-b