Is it possible that
L1 U L2
= regular language ?
Yes, Possible.
A simple case is: if L1 is sub-set of L2 then L1 U L2
will be regular (=L2
), for example: L1 : { anbn
| where n >= 0
} and L2 = (a + b)*
is it possible that
L1 * L2
= regular language ?
No, Concatenation of a context-free and Regular will be context-free (because constraint in pattern of L1 is still there in L1 * L2
).
Adding a reference: CS 273: Closure Properties for Context-Free Languages