9. EXTRA CREDIT: One of the founders of evolutionary computation, Laurence Fogel, tried to see if you could evolve finite state machines to do computations by a combination of mutation and selection of the fittest (Fogel et al., 1965), and out of this came the field called Evolutionary Programming. We will try mutating the finite state machine in Table 3, p. 861 (given below) to see how it changes its computation S S1 0 82 83 S40 0 s3SS00 0 s4 S3S0 0 If we keep the number of states fixed at 5, and keep the same input and output alphabets, then mutations can consist of changing entries of the transition func- tion f, or the output function g. Since the output doesn't affect the sequence of states, we will mutate the states. (a) Trace the operation of the machine (1) when given an input string 111111. By 'trace' I mean give the new state and the output. For example, for the input 010 we would get 9. EXTRA CREDIT: One of the founders of evolutionary computation, Laurence Fogel, tried to see if you could evolve finite state machines to do computations by a combination of mutation and selection of the fittest (Fogel et al., 1965), and out of this came the field called Evolutionary Programming. We will try mutating the finite state machine in Table 3, p. 861 (given below) to see how it changes its computation S S1 0 82 83 S40 0 s3SS00 0 s4 S3S0 0 If we keep the number of states fixed at 5, and keep the same input and output alphabets, then mutations can consist of changing entries of the transition func- tion f, or the output function g. Since the output doesn't affect the sequence of states, we will mutate the states. (a) Trace the operation of the machine (1) when given an input string 111111. By 'trace' I mean give the new state and the output. For example, for the input 010 we would get