NonDeterministic Finite Automata 1 Nondeterministic Finite Automaton NFA
![Non-Deterministic Finite Automata 1 Non-Deterministic Finite Automata 1](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-1.jpg)
![Nondeterministic Finite Automaton (NFA) Alphabet = 2 Nondeterministic Finite Automaton (NFA) Alphabet = 2](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-2.jpg)
![Alphabet = Two choices 3 Alphabet = Two choices 3](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-3.jpg)
![Alphabet = Two choices No transition 4 Alphabet = Two choices No transition 4](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-4.jpg)
![First Choice 5 First Choice 5](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-5.jpg)
![First Choice 6 First Choice 6](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-6.jpg)
![First Choice 7 First Choice 7](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-7.jpg)
![First Choice All input is consumed “accept” 8 First Choice All input is consumed “accept” 8](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-8.jpg)
![Second Choice 9 Second Choice 9](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-9.jpg)
![Second Choice 10 Second Choice 10](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-10.jpg)
![Second Choice No transition: the automaton hangs 11 Second Choice No transition: the automaton hangs 11](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-11.jpg)
![Second Choice Input cannot be consumed “reject” 12 Second Choice Input cannot be consumed “reject” 12](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-12.jpg)
![An NFA accepts a string: when there is a computation of the NFA that An NFA accepts a string: when there is a computation of the NFA that](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-13.jpg)
![Example is accepted by the NFA: “accept” because this computation accepts “reject” 14 Example is accepted by the NFA: “accept” because this computation accepts “reject” 14](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-14.jpg)
![Rejection example 15 Rejection example 15](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-15.jpg)
![First Choice 16 First Choice 16](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-16.jpg)
![First Choice “reject” 17 First Choice “reject” 17](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-17.jpg)
![Second Choice 18 Second Choice 18](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-18.jpg)
![Second Choice 19 Second Choice 19](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-19.jpg)
![Second Choice “reject” 20 Second Choice “reject” 20](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-20.jpg)
![An NFA rejects a string: when there is no computation of the NFA that An NFA rejects a string: when there is no computation of the NFA that](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-21.jpg)
![Example is rejected by the NFA: “reject” All possible computations lead to rejection 22 Example is rejected by the NFA: “reject” All possible computations lead to rejection 22](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-22.jpg)
![Rejection example 23 Rejection example 23](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-23.jpg)
![First Choice 24 First Choice 24](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-24.jpg)
![First Choice No transition: the automaton hangs 25 First Choice No transition: the automaton hangs 25](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-25.jpg)
![First Choice Input cannot be consumed “reject” 26 First Choice Input cannot be consumed “reject” 26](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-26.jpg)
![Second Choice 27 Second Choice 27](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-27.jpg)
![Second Choice 28 Second Choice 28](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-28.jpg)
![Second Choice No transition: the automaton hangs 29 Second Choice No transition: the automaton hangs 29](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-29.jpg)
![Second Choice Input cannot be consumed “reject” 30 Second Choice Input cannot be consumed “reject” 30](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-30.jpg)
![is rejected by the NFA: “reject” All possible computations lead to rejection 31 is rejected by the NFA: “reject” All possible computations lead to rejection 31](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-31.jpg)
![Language accepted: 32 Language accepted: 32](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-32.jpg)
![Lambda Transitions 33 Lambda Transitions 33](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-33.jpg)
![34 34](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-34.jpg)
![35 35](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-35.jpg)
![(read head does not move) 36 (read head does not move) 36](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-36.jpg)
![37 37](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-37.jpg)
![all input is consumed “accept” String is accepted 38 all input is consumed “accept” String is accepted 38](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-38.jpg)
![Rejection Example 39 Rejection Example 39](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-39.jpg)
![40 40](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-40.jpg)
![(read head doesn’t move) 41 (read head doesn’t move) 41](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-41.jpg)
![No transition: the automaton hangs 42 No transition: the automaton hangs 42](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-42.jpg)
![Input cannot be consumed “reject” String is rejected 43 Input cannot be consumed “reject” String is rejected 43](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-43.jpg)
![Language accepted: 44 Language accepted: 44](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-44.jpg)
![Another NFA Example 45 Another NFA Example 45](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-45.jpg)
![46 46](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-46.jpg)
![47 47](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-47.jpg)
![48 48](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-48.jpg)
![“accept” 49 “accept” 49](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-49.jpg)
![Another String 50 Another String 50](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-50.jpg)
![51 51](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-51.jpg)
![52 52](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-52.jpg)
![53 53](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-53.jpg)
![54 54](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-54.jpg)
![55 55](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-55.jpg)
![56 56](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-56.jpg)
![“accept” 57 “accept” 57](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-57.jpg)
![Language accepted 58 Language accepted 58](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-58.jpg)
![Another NFA Example 59 Another NFA Example 59](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-59.jpg)
![Language accepted (redundant state) 60 Language accepted (redundant state) 60](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-60.jpg)
![Remarks: • The symbol never appears on the input tape • Simple automata: 61 Remarks: • The symbol never appears on the input tape • Simple automata: 61](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-61.jpg)
![• NFAs are interesting because we can express languages easier than FAs NFA • NFAs are interesting because we can express languages easier than FAs NFA](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-62.jpg)
![Formal Definition of NFAs Set of states, i. e. Input aplhabet, i. e. Transition Formal Definition of NFAs Set of states, i. e. Input aplhabet, i. e. Transition](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-63.jpg)
![Transition Function 64 Transition Function 64](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-64.jpg)
![65 65](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-65.jpg)
![66 66](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-66.jpg)
![67 67](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-67.jpg)
![Extended Transition Function 68 Extended Transition Function 68](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-68.jpg)
![69 69](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-69.jpg)
![70 70](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-70.jpg)
![Formally : there is a walk from with label to 71 Formally : there is a walk from with label to 71](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-71.jpg)
![The Language of an NFA 72 The Language of an NFA 72](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-72.jpg)
![73 73](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-73.jpg)
![74 74](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-74.jpg)
![75 75](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-75.jpg)
![76 76](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-76.jpg)
![Formally The language accepted by NFA is: where and there is some (accepting state) Formally The language accepted by NFA is: where and there is some (accepting state)](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-77.jpg)
![78 78](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-78.jpg)
- Slides: 78
![NonDeterministic Finite Automata 1 Non-Deterministic Finite Automata 1](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-1.jpg)
Non-Deterministic Finite Automata 1
![Nondeterministic Finite Automaton NFA Alphabet 2 Nondeterministic Finite Automaton (NFA) Alphabet = 2](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-2.jpg)
Nondeterministic Finite Automaton (NFA) Alphabet = 2
![Alphabet Two choices 3 Alphabet = Two choices 3](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-3.jpg)
Alphabet = Two choices 3
![Alphabet Two choices No transition 4 Alphabet = Two choices No transition 4](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-4.jpg)
Alphabet = Two choices No transition 4
![First Choice 5 First Choice 5](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-5.jpg)
First Choice 5
![First Choice 6 First Choice 6](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-6.jpg)
First Choice 6
![First Choice 7 First Choice 7](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-7.jpg)
First Choice 7
![First Choice All input is consumed accept 8 First Choice All input is consumed “accept” 8](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-8.jpg)
First Choice All input is consumed “accept” 8
![Second Choice 9 Second Choice 9](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-9.jpg)
Second Choice 9
![Second Choice 10 Second Choice 10](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-10.jpg)
Second Choice 10
![Second Choice No transition the automaton hangs 11 Second Choice No transition: the automaton hangs 11](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-11.jpg)
Second Choice No transition: the automaton hangs 11
![Second Choice Input cannot be consumed reject 12 Second Choice Input cannot be consumed “reject” 12](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-12.jpg)
Second Choice Input cannot be consumed “reject” 12
![An NFA accepts a string when there is a computation of the NFA that An NFA accepts a string: when there is a computation of the NFA that](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-13.jpg)
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 13
![Example is accepted by the NFA accept because this computation accepts reject 14 Example is accepted by the NFA: “accept” because this computation accepts “reject” 14](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-14.jpg)
Example is accepted by the NFA: “accept” because this computation accepts “reject” 14
![Rejection example 15 Rejection example 15](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-15.jpg)
Rejection example 15
![First Choice 16 First Choice 16](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-16.jpg)
First Choice 16
![First Choice reject 17 First Choice “reject” 17](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-17.jpg)
First Choice “reject” 17
![Second Choice 18 Second Choice 18](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-18.jpg)
Second Choice 18
![Second Choice 19 Second Choice 19](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-19.jpg)
Second Choice 19
![Second Choice reject 20 Second Choice “reject” 20](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-20.jpg)
Second Choice “reject” 20
![An NFA rejects a string when there is no computation of the NFA that An NFA rejects a string: when there is no computation of the NFA that](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-21.jpg)
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 21
![Example is rejected by the NFA reject All possible computations lead to rejection 22 Example is rejected by the NFA: “reject” All possible computations lead to rejection 22](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-22.jpg)
Example is rejected by the NFA: “reject” All possible computations lead to rejection 22
![Rejection example 23 Rejection example 23](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-23.jpg)
Rejection example 23
![First Choice 24 First Choice 24](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-24.jpg)
First Choice 24
![First Choice No transition the automaton hangs 25 First Choice No transition: the automaton hangs 25](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-25.jpg)
First Choice No transition: the automaton hangs 25
![First Choice Input cannot be consumed reject 26 First Choice Input cannot be consumed “reject” 26](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-26.jpg)
First Choice Input cannot be consumed “reject” 26
![Second Choice 27 Second Choice 27](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-27.jpg)
Second Choice 27
![Second Choice 28 Second Choice 28](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-28.jpg)
Second Choice 28
![Second Choice No transition the automaton hangs 29 Second Choice No transition: the automaton hangs 29](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-29.jpg)
Second Choice No transition: the automaton hangs 29
![Second Choice Input cannot be consumed reject 30 Second Choice Input cannot be consumed “reject” 30](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-30.jpg)
Second Choice Input cannot be consumed “reject” 30
![is rejected by the NFA reject All possible computations lead to rejection 31 is rejected by the NFA: “reject” All possible computations lead to rejection 31](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-31.jpg)
is rejected by the NFA: “reject” All possible computations lead to rejection 31
![Language accepted 32 Language accepted: 32](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-32.jpg)
Language accepted: 32
![Lambda Transitions 33 Lambda Transitions 33](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-33.jpg)
Lambda Transitions 33
![34 34](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-34.jpg)
34
![35 35](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-35.jpg)
35
![read head does not move 36 (read head does not move) 36](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-36.jpg)
(read head does not move) 36
![37 37](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-37.jpg)
37
![all input is consumed accept String is accepted 38 all input is consumed “accept” String is accepted 38](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-38.jpg)
all input is consumed “accept” String is accepted 38
![Rejection Example 39 Rejection Example 39](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-39.jpg)
Rejection Example 39
![40 40](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-40.jpg)
40
![read head doesnt move 41 (read head doesn’t move) 41](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-41.jpg)
(read head doesn’t move) 41
![No transition the automaton hangs 42 No transition: the automaton hangs 42](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-42.jpg)
No transition: the automaton hangs 42
![Input cannot be consumed reject String is rejected 43 Input cannot be consumed “reject” String is rejected 43](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-43.jpg)
Input cannot be consumed “reject” String is rejected 43
![Language accepted 44 Language accepted: 44](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-44.jpg)
Language accepted: 44
![Another NFA Example 45 Another NFA Example 45](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-45.jpg)
Another NFA Example 45
![46 46](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-46.jpg)
46
![47 47](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-47.jpg)
47
![48 48](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-48.jpg)
48
![accept 49 “accept” 49](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-49.jpg)
“accept” 49
![Another String 50 Another String 50](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-50.jpg)
Another String 50
![51 51](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-51.jpg)
51
![52 52](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-52.jpg)
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![accept 57 “accept” 57](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-57.jpg)
“accept” 57
![Language accepted 58 Language accepted 58](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-58.jpg)
Language accepted 58
![Another NFA Example 59 Another NFA Example 59](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-59.jpg)
Another NFA Example 59
![Language accepted redundant state 60 Language accepted (redundant state) 60](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-60.jpg)
Language accepted (redundant state) 60
![Remarks The symbol never appears on the input tape Simple automata 61 Remarks: • The symbol never appears on the input tape • Simple automata: 61](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-61.jpg)
Remarks: • The symbol never appears on the input tape • Simple automata: 61
![NFAs are interesting because we can express languages easier than FAs NFA • NFAs are interesting because we can express languages easier than FAs NFA](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-62.jpg)
• NFAs are interesting because we can express languages easier than FAs NFA FA 62
![Formal Definition of NFAs Set of states i e Input aplhabet i e Transition Formal Definition of NFAs Set of states, i. e. Input aplhabet, i. e. Transition](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-63.jpg)
Formal Definition of NFAs Set of states, i. e. Input aplhabet, i. e. Transition function Initial state Accepting states 63
![Transition Function 64 Transition Function 64](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-64.jpg)
Transition Function 64
![65 65](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-65.jpg)
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67
![Extended Transition Function 68 Extended Transition Function 68](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-68.jpg)
Extended Transition Function 68
![69 69](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-69.jpg)
69
![70 70](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-70.jpg)
70
![Formally there is a walk from with label to 71 Formally : there is a walk from with label to 71](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-71.jpg)
Formally : there is a walk from with label to 71
![The Language of an NFA 72 The Language of an NFA 72](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-72.jpg)
The Language of an NFA 72
![73 73](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-73.jpg)
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76
![Formally The language accepted by NFA is where and there is some accepting state Formally The language accepted by NFA is: where and there is some (accepting state)](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-77.jpg)
Formally The language accepted by NFA is: where and there is some (accepting state) 77
![78 78](https://slidetodoc.com/presentation_image_h2/67dda53c0129e07409cd93d7d3d9cbbc/image-78.jpg)
78
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Unit 2
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