Student email questions and responses

Hi XXX,

Nice question.  Generally, closure happens one way.
Suppose L = AB, where L is regular and A, B are languages.
Your question is: do both A and B have to be regular?
No, for example, take A = {a^n b^n : n >= 0} and B = {a,b}*.
Note that L = {a,b}* since the empty string is in A.

A challenge: find A and B that are both non-regular and
yet such that AB is regular.

Cheers,
Frank R.

| Hi Dr. Rusky,
|
| I have a question about the RL closure Properties 
| (relating to question 2.3.6 in the homework). I was just wondering 
| if the closure holds both ways? For example, if w=xy and w can be 
| represented as a FA, does that mean X and y can also? Or can we not 
| conclude that. I have tried, but i haven't found a case where this 
| doesn't work...
| Thanks, XXX.