System #1:

Pattern Recognizer (using a state transition diagram) Consider a Pattern Recognizer that accepts single digit inputs (0 or 1) each time unit and outputs a NO (or 0) until the pattern 101101 has been seen in the stream of inputs then a YES (or 1) will be output. [Hint: draw a state transition diagram to define the states and next state behavior.]

Answer:

Z = (SZ, IZ, OZ, NZ, RZ)

SZ = {None, 1, 10, 101, 1011, 10110, 101101}

IZ = {1, 0}

OZ = {YES, NO}

NZ = {((None, 0), None), ((None, 1), 1), ((1, 1), 1), ((1, 0), 10), ((10, 1), 101), ((10, 0), None), ((101, 1), 1011), ((101, 0), 10), ((1011, 1), 1), ((1011, 0), 10110), ((10110, 1), 101101), ((10110, 0), None), ((101101, 0), None), ((101101, 1), None)}

RZ = {(x, q): x SZ; q OZ; if x = ( 1, 0, 1, 1, 0,

q = YES, q = NO}

Question ??

f1={(0,1),(1,1),(2,0),(3,1),(4,1),(5,0),(6,1),(7,0),(8,1),(9,1),(10,0),(11,1),(12,1),(13,0), (14,0), (15,0),(16,1)} f3={(0,0),(1,1),(2,0),(3,1),(4,1),(5,0),(6,1),(7,0),(8,1),(9,0),(10,0),(11,1),(12,1),(13,0), (14,1), (15,0),(16,0)}

Run two system experiments to demonstrate that your pattern recognizer works. Use the following input trajectories:

Start your system in the state (initial) that represents None of the digits of the pattern being observed and run your experiments for 16 time steps.

Develop the model and run both experiments. Prepare a written report with graphs (scope) showing the input and output trajectories, and a screen shot of your state machine and model.