finite automata

there are two types of finite automata:

given 2 automata, we can construct a third that only accepts if they both accept. given automata $\text{[math]}$ , we construct $\text{[math]}$ as follows:
$\text{[math]}$ we have that $\text{[math]}$ accepts a sequence only if $\text{[math]}$ and $\text{[math]}$ both accept it. this technique is called product construction.