Question

$\text{Consider a DFA over}\sum$= {a, b}
$\text{accepting all strings which have number}$
$\text{of a's divisible by 6 and number of b's}$
$\text{divisible by 8. What is the minimum}$
$\text{numberof states that the DFA will have?}$

Answer 1

A DFA over $\sum$ = {a, b} accepting all strings which have no. of a's divisible by 6 and number of b's divisible by 8 is a grid machine (product automata) having 6 $\times$ 8 = 48 states.