Define next state function in terms of description and as a state transition diagram or a mathematical function or pseudo code, define time scale for your model.

Pattern Recognizer (as a register)

A Pattern Recognizer that accepts single digit inputs (0 or a 1) each time unit and outputs a NO (as a 0) until the pattern 101101 has been seen in the stream of inputs then a YES (as a 1) will be output.

A register that hold the last several digits received and shifts in a new digit when received and shift out the oldest digit.

Answer:

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

IZ = {0, 1}

SZ = {x1, x2, x3, x4, x5, x6}; xk={0, 1}, j=1, 2, 3, 4, 5, 6}

OZ = {YES, NO}

NZ={((x, p), y):x SZ;P IZ;y SZ;if x=(x1, x2, x3, x4, x5, x6), then y=(P, x2, x3, x4, x5, x6)}

RZ = {(x, q):x SZ;q OZ ;if x=(1, 0, 1, 1, 0, 1) then q=YES, else q=NO}

Question: ?

Run two system experiments to demonstrate that your pattern recognizer works. Use the following input trajectories: 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)} f2={(0,0),(1,1),(2,1),(3,1),(4,0),(5,0),(6,1),(7,1),(8,0),(9,0),(10,1),(11,1),(12,0),(13,0), (14,0), (15,1),(16,1)} Start your system in the state (initial) that represents None, or the (0,0,0,0,0,0,0) state, of the digits of the pattern have been observed and run your experiments for 16 time steps