If 2 L spanned from the bit alphabet. L1 = 000 L2 = 0 *1 * If we concatenate them L1L2 = 0000 *1 * I believe these 2 languages are regular because of a trivial DFA. But if you pump on L1... it would take you out of the language A non regular concatenated with a regular language is not a regular language.
What are your thoughts?
The concatenation of two regular languages is always a regular language. The simplest way to prove this is to imagine NFAs for each language, and then imagine hooking these up in sequence by having all of the accepting states of the first NFA empty-transition (lambda, epsilon) over the initial state of the second NFA. That gives you an NFA for the concatenation.
If we concatenate a regular and a non-regular language, the situation is more complicated: we might get a regular or a non-regular language, depending on the circumstances.