This document is a tutorial on automata theory and logic pattern detection in Mealy machines. It discusses designing Mealy machines and sequential circuits to detect patterns such as 010 and 101 for both overlap and non-overlap conditions. It provides examples of Mealy machines that detect these patterns in input strings and minimize the machines. It also discusses implementing detectors for these Mealy machines using sequential circuits and constructing Karnaugh maps.

1. Automata Theory and Logic
Pattern detection in Mealy machine
A TUTORIAL
BY
ANIMESH CHATURVEDI
AT
INDIAN INSTITUTE OF TECHNOLOGY INDORE (IIT-I)

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

3. 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

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

5. 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

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

7. Pattern detect for 010 (overlap)
Design a sequential circuit to implement the detector of above mealy machine.
D0 = q1X + q0q͞1 X͞

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

9. 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

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

11. 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

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

13. 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

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

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

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

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

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

19. 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’

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

21. 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

22. Pattern detect for 010 (non-overlap)
Design a sequential circuit to implement the detector of above mealy machine.
where A` is initial state

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

24. 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.

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

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

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

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

29. 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