Finite State Machine for Synchronous Circuit
Assuming:


Q0 is the output of the DFF on the left,
Q1 is the output of the DFF on the right,
Q0+ = Q0* = Q0 next,
Q1+ = Q1* = Q1 next


We can derive expressions for the values Q0*, Q1*, F and G from observations of the circuit.


F = Q0 (connected to output of Q0 DFF)
G = Q1 (connected to output of Q1 DFF)
Q1* = Q0 (connected to output of Q0 DFF)
Q0* = ~Q1 (connected to inverted output of Q1 DFF)


You may notice that all of the above equations only depend on the Q0 and Q1 state registers. This means this is a Moore FSM since the output depends only on the present state. We can build the entire truth table from just the Q0 and Q1 states on the left side:

Truth Table

Q1 Q0 | Q1* Q0* G F
-------------------
0  0  | 0   1   0 0
0  1  | 1   1   0 1
1  0  | 0   0   1 0
1  1  | 1   0   1 1