Create a finite state machine that recognizes the input strings arc, acre, and car by outputting a 1 (otherwise output 0).

The input alphabet is {a, c, e, r}. The output alphabet is {0, 1}.

The input stream may be any length, beginning with any arbitrary sequence of the input alphabet.

The FSM should not terminate. The FSM should recognize overlapping tokens (input strings).

1) Draw the FSM.

2) Create the state transition table.

3) What is the sequence of states your FSM will go through when the string

aacarccacree is input?

Grading Rubric

Parts a and b are worth 40 points each. Part c is worth 20 points.

The FSM should be completely specified. The FSM must include both inputs and outputs for each transition.

The state transition tables should specify both outputs and next states. Please use the same format for the state transition table as in the lecture slides!

Each incorrect state or transition (judged against the provided minimal FSM in the example solution) will count a proportional number of points (count of states + count of transitions). Your FSM need not be minimal.