1. CSE322 Definition and description of finite Automata
Lecture #1

2. Definition
An automaton is defined as a system where energy, materials and information are transformed, transmitted and used for performing some functions without direct participation of man.

3. Formal Definition
Finite Automaton (FA)
Finite Automaton (FA)
: set of states
: input alphabet
: transition function
: initial state
: set of accepting states

4. Input alphabet
Input alphabet

5. Set of States
Set of States

6. Initial State
Initial State

7. Set of Accepting States

8. Non-Deterministic Finite Automata

9. Nondeterministic Finite Automaton
Alphabet =

10. Alphabet =
Two choices

11. Alphabet =
Two choices
No transition
No transition

12. First Choice

13. First Choice

14. First Choice

15. First Choice
All input is consumed
“accept”

16. Second Choice

17. Second Choice

18. Second Choice
No transition:
the automaton hangs

19. Second Choice
Input cannot be consumed
“reject”

20. An NFA accepts a string:
when there is a computation of the
NFA that accepts the string
There is a computation:
all the input is consumed and the automaton
is in an accepting state

21. Example is accepted by the NFA: “accept” “reject” because this
computation
accepts

22. Rejection example

23. First Choice

24. First Choice
“reject”

25. Second Choice

26. Second Choice

27. Second Choice
“reject”

28. OR An NFA rejects a string: when there is no computation of the
NFA that accepts the string.
For each computation:
All the input is consumed and the
automaton is in a non final state OR
The input cannot be consumed

29. Example is rejected by the NFA: “reject” “reject”
All possible computations lead to rejection

30. Rejection example

31. First Choice

32. First Choice
No transition:
the automaton hangs

33. First Choice
Input cannot be consumed
“reject”

34. Second Choice

35. Second Choice

36. Second Choice
No transition:
the automaton hangs

37. Second Choice
Input cannot be consumed
“reject”

38. is rejected by the NFA:
“reject”
“reject”
All possible computations lead to rejection

39. Language accepted:

40. Lambda Transitions

43. (read head does not move)

45. all input is consumed
“accept”
String is accepted

46. Rejection Example

48. (read head doesn’t move)

49. No transition:
the automaton hangs

50. Input cannot be consumed
“reject”
String is rejected

51. Language accepted:

52. Another NFA Example

56. “accept”

57. Another String

64. “accept”

65. Language accepted

66. Another NFA Example

67. Language accepted
(redundant
state)

68. Remarks:
The symbol never appears on the
input tape
Simple automata:

69. NFAs are interesting because we can
express languages easier than FAs
NFA FA

70. Formal Definition of NFAs
Set of states, i.e.
Input aplhabet, i.e.
Transition function
Initial state
Accepting states

71. Transition Function

75. Extended Transition Function

78. Formally
: there is a walk from to
with label

79. The Language of an NFA