For the specific example Finite State Control C as shown above, give formulas for | C (0n) | and | C (1n) | in terms of n. What strings are compressed by C?

The diagram above denotes the FSC C=(Q,,,s), where - Q={0,1,2,3} - (q,0)=(q+1)mod4 for all qQ; - (q,1)=0 for all qQ; - (q,0)={,0,ifq2ifq=3 - (q,1)=10q1 for all qQ. Note that each transition arrow is labeled by b/y, where b is the input bit producing the transition and y is the output string produced by the transition. Intuitively, an FSC compresses an input string w if C(w) is significantly less than w