Regular expression or automata for language with odd number of 0's and odd number of 1's Let $\Sigma=\{0,1\}$ and $L=\{u \in \Sigma^* : u \text{ has odd number of 0's and odd number of 1's}\}$. How can I build a regular expression or an automaton for this language? I have no idea, and I guess $L$ is not regular, but I haven't been able to prove it with the pumping lemma.

If it is not regular, can you give me a hint to prove it?
Hint: You are trying to solve two problems (i.e., odd number of zeros and odd number of ones) at once. Try to solve each separately instead and then combine the solutions appropriately.