lecture 5.ppt by 5th SEM LPU Lecture PPT

CSe 322

1. CSE322
Mealy and Moore Machine
Lecture #4

2. Null Transition
•An NFA with null transition is allowed to make
transition not only on input from the alphabet
but also with null input, i.e. without any input
symbol. This transition without input is called
null transition.

3. Null Transition

4. Null Transition

5. 1
q
2
q
3q
a
a
a
0q
Language accepted: }{aaL

6. Lambda Transitions
1
q
3
qa
0
q 
2
qa

7. aa
1
q
3
qa
0
q 
2
qa

8. aa
1
q
3
qa
0
q 
2
qa

9. aa
1
q
3
qa
0
q 
2
qa
(read head does not move)

10. aa
1
q
3
qa
0
q 
2
qa

11. aa
1
q
3
qa
0
q 
2
qa
“accept”
String is accepted
aa
all input is consumed

12. aa
1
q
3
qa
0
q 
2
qa
Rejection Example
a

13. aa
1
q
3
qa
0
q 
2
qa
a

14. aa
1
q
3
qa
0
q 
2
qa
(read head doesn’t move)
a

15. aa
1
q
3
qa
0
q 
2
qa
a
No transition:
the automaton hangs

16. aa
1
q
3
qa
0
q 
2
qa
“reject”
String is rejected
aaa
a
Input cannot be consumed

17. Language accepted: }{aaL
1
q
3
qa
0
q 
2
qa

18. Another NFA Example
0q 1q
2qa b 

3
q

19. How to accept a string

20. How to accept a string

21. ab
0q 1q
2qa b 

3
q

22. 0q 2qa b 

3
q
ab
1
q

23. ab
0q 1q a b 

3
q
2
q

24. ab
0q 1q a b 

3
q
2
q
“accept”

25. 0q
a b 

ab
Another String
ab
1
q
2
q
3
q

26. 0q
a b 

abab
1
q
2
q
3
q

27. 0q
a b 

abab
1
q
2
q
3
q

28. 0q
a b 

abab
1
q
2
q
3
q

29. 0q
a b 

abab
1
q
2
q
3
q

30. 0q
a b 

abab
1
q
2
q
3
q

31. 0q
a b 

abab
1
q
2
q
3
q

32. abab
0q
a b 

1
q
2
q
3
q
“accept”

33.  




ab
ababababababL ...,,,
Language accepted
0q 1q
2qa b 

3
q

34. Another NFA Example
0
q 1
q
2
q
0
1
1,0


35. { }
{}*10=
...,101010,1010,10,λ=)(ML
0
q 1
q
2
q
0
1
1,0

Language accepted
(redundant
state)

36. In finite Automata acceptability was decided on the basis of reach
ability of the final state by initial state.
This restriction are removed and new model is given in which
output can be chosen from some other alphabet.
The value of the output function Z(t) is a function of present state
q(t) and the present input x(t)
 Z(t) = λ(q(t), x(t)) Mealy Machine
 The value of the output function Z(t) is a function of present state
q(t) only and is independent of the current input
 Z(t) = λ(q(t)) Moore Machine
Mealy and Moore Model

37. Moore Machine is six-tuple (Q,∑,∆,δ,λ,q
0
):
(i)Q is a finite set of states
(ii)∑ is the input alphabet
(iii)∆ is the output alphabet
(iv)δ is the transition function from ∑ X Q into Q
(v)λ is the output function mapping Q into ∆ and
(vi) q
0 is the initial state
Moore Machine

38. Mealy Machine is six-tuple (Q,∑,∆,δ,λ,q
0
):
(i)Q is a finite set of states
(ii)∑ is the input alphabet
(iii)∆ is the output alphabet
(iv)δ is the transition function from ∑ X Q into Q
(v)λ is the output function mapping ∑ X Q into ∆ and
(vi) q
0 is the initial state
Mealy Machine

39. Example of Moore Machine

40. Example of Mealy Machine

41. Transforming Mealy to Moore Machine

42. Solution

43. Transforming Moore to Mealy Machine

44. Solution

46. Solution

47. Answer Justification
•Here there is no output associated with q1 so,
It will be ^.
•q2 is associated with 2 outputs z1 and z2 so 2
states will be considered q21,q22.
•q3 is associated with 2 outputs z1 and z2 so 2
states will be considered q31,q32

48. Answer

50. Solution

51. Convert it to Moore Machine

52. Convert it to mealy machine