Using formulas for ri jk find a regular expression for the f

Using formulas for r_i, j^k find a regular expression for the following dfa:

Solution

The regular expression would be

0*10*(01)*1(0,1)*

as here 0 is recursive input to q1 then one single input 1 to q2 then a recursive input 0,1 to q3 hence (0,1)* then recursive input 0 to q2 hence 0* then 1 as single input to q4 then (0,1) recursive input to q4 hence (0,1)*.