I have these two problems about regular expressions, can you help me?
1) Prove (ab)∗a = a(ba)∗.
I already proved this using induction and the definition of the kleene star * but I want to prove it now using NFAs, I drawed the NFAs for each but they don't seem to be equal from the picture and I'm stuck there.
2) Prove 0∗(11)∗((00)∗0∗(11)∗)∗0 = (0+11+00)∗0
For this I was think of creating a NFA for each side then converting them to a DFA and prove them equal using the product automata but since each side is very big that sounds like too much word to do by hand and I was wondering if there is a faster way.
Thanks in advance
