Automata Theory and LogicPattern detection in Mealy machine

A TUTORIAL

BY

ANIMESH CHATURVEDI

AT

INDIAN INSTITUTE OF TECHNOLOGY INDORE ( I IT - I )

Pattern detect for 010 (overlap)Design a mealy machine to detect count of occurrence of string 010 for overlap condition?

Pattern detect for 010 (overlap)Design a mealy machine to detect count of occurrence of string 010 for overlap condition?

Input: 1010101

Output: 0001010

Minimize this into 3 states by joining B and D

Pattern detect for 010 (overlap)Design a sequential circuit to implement the detector of above mealy machine.

Pattern detect for 010 (overlap)Design a sequential circuit to implement the detector of above mealy machine.

Input: 1010101

Output: 0001010

Minimize this into 3 states by joining B and D

Pattern detect for 010 (overlap)Design a sequential circuit to implement the detector of above mealy machine.

Pattern detect for 010 (overlap)Design a sequential circuit to implement the detector of above mealy machine.

D0 = q1X + q0q1͞ X ͞

Pattern detect for 101 (overlap)Design a mealy machine to detect count of occurrence of string 101 for overlap condition?

Pattern detect for 101 (overlap)Design a mealy machine to detect count of occurrence of string 101 for overlap condition?

Input: 1010101

Output: 0010101

where A is the initial state

Minimize this into 3 states by joining B and D

Pattern detector for 101 (non-overlap)Design a mealy machine to detect count of occurrence of string 101 for non-overlap condition?

Pattern detect for 101 (overlap)Design a mealy machine to detect count of occurrence of string 101 for overlap condition?

where A is the initial state

Pattern detect for 101 (non-overlap)Design a sequential circuit to implement the detector of above mealy machine.

Pattern detector for 101 (non-overlap)Design a mealy machine to detect count of occurrence of string 101 for non-overlap condition?

Input: 1010101

Output: 0010001

Minimize this into 3 states by joining B and D

Pattern detect for 101 (non-overlap)Design a sequential circuit to implement the detector of above mealy machine.

Pattern detect for 101 (non-overlap)Design a sequential circuit to implement the detector of above mealy machine.

Pattern detect for 101 (non-overlap)Design a sequential circuit to implement the detector of above mealy machine.

Pattern detect for 101 (non-overlap)Design a sequential circuit to implement the detector of above mealy machine.

Pattern detect for 010 (non-overlap)Design a mealy machine to detect count of occurrence of string 010 for non-overlap condition?

Pattern detect for 010 (non-overlap)Design a mealy machine to detect count of occurrence of string 010 for non-overlap condition?

Input: 1010101

Output: 0001000

where A` is initial state

Minimize this into 3 states by joining B’ and D’

Pattern detect for 010 (non-overlap)Design a sequential circuit to implement the detector of above mealy machine.

Pattern detect for 010 (non-overlap)Design a sequential circuit to implement the detector of above mealy machine.

Input: 1010101

Output: 0001000 where A` is initial state

Pattern detect for 010 (non-overlap)Design a sequential circuit to implement the detector of above mealy machine.

where A` is initial state

Pattern detect for 010 & 101 (overlap)Design a mealy machine to detect count of occurrence of both string 010 and 101 for overlap condition?

Pattern detect for 010 & 101 (overlap)Design a mealy machine to detect count of occurrence of both string 010 and 010 for overlap condition?

Input: 1010101

Output: 0011111

Is it minimized? If not then minimize it.

Pattern detect for 010 & 101 (overlap)Design a sequential circuit to implement the detector of above mealy machine.

Pattern detect for 010 & 101 (overlap)Design a sequential circuit to implement the detector of above mealy machine.

Pattern detect for 010 & 101 (overlap)Design a sequential circuit to implement the detector of above mealy machine.

Pattern detect for 010 & 101 (overlap)Design a sequential circuit to implement the detector of above mealy machine.

Pattern detect for 010 & 101 (overlap)Design a sequential circuit to implement the detector of above mealy machine.

Find D0, D1, D2 and Z by building 4 × 4 Karnaugh map for each of them using q0, q1, q2 and X