NonDeterministic Finite Automata Prof Busch LSU 1 Nondeterministic
![Non-Deterministic Finite Automata Prof. Busch - LSU 1 Non-Deterministic Finite Automata Prof. Busch - LSU 1](https://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-1.jpg)
Non-Deterministic Finite Automata Prof. Busch - LSU 1
![Nondeterministic Finite Automaton (NFA) Alphabet = Prof. Busch - LSU 2 Nondeterministic Finite Automaton (NFA) Alphabet = Prof. Busch - LSU 2](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-2.jpg)
Nondeterministic Finite Automaton (NFA) Alphabet = Prof. Busch - LSU 2
![Alphabet = Two choices No transition Prof. Busch - LSU 3 Alphabet = Two choices No transition Prof. Busch - LSU 3](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-3.jpg)
Alphabet = Two choices No transition Prof. Busch - LSU 3
![First Choice Prof. Busch - LSU 4 First Choice Prof. Busch - LSU 4](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-4.jpg)
First Choice Prof. Busch - LSU 4
![First Choice Prof. Busch - LSU 5 First Choice Prof. Busch - LSU 5](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-5.jpg)
First Choice Prof. Busch - LSU 5
![First Choice All input is consumed “accept” Prof. Busch - LSU 6 First Choice All input is consumed “accept” Prof. Busch - LSU 6](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-6.jpg)
First Choice All input is consumed “accept” Prof. Busch - LSU 6
![Second Choice Prof. Busch - LSU 7 Second Choice Prof. Busch - LSU 7](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-7.jpg)
Second Choice Prof. Busch - LSU 7
![Second Choice Input cannot be consumed Automaton Halts “reject” Prof. Busch - LSU 8 Second Choice Input cannot be consumed Automaton Halts “reject” Prof. Busch - LSU 8](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-8.jpg)
Second Choice Input cannot be consumed Automaton Halts “reject” Prof. Busch - LSU 8
![An NFA accepts a string: if there is a computation of the NFA that An NFA accepts a string: if there is a computation of the NFA that](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-9.jpg)
An NFA accepts a string: if there is a computation of the NFA that accepts the string i. e. , all the input string is processed and the automaton is in an accepting state Prof. Busch - LSU 9
![is accepted by the NFA: “accept” because this computation accepts “reject” this computation is is accepted by the NFA: “accept” because this computation accepts “reject” this computation is](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-10.jpg)
is accepted by the NFA: “accept” because this computation accepts “reject” this computation is ignored Prof. Busch - LSU 10
![Rejection example Prof. Busch - LSU 11 Rejection example Prof. Busch - LSU 11](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-11.jpg)
Rejection example Prof. Busch - LSU 11
![First Choice “reject” Prof. Busch - LSU 12 First Choice “reject” Prof. Busch - LSU 12](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-12.jpg)
First Choice “reject” Prof. Busch - LSU 12
![Second Choice Prof. Busch - LSU 13 Second Choice Prof. Busch - LSU 13](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-13.jpg)
Second Choice Prof. Busch - LSU 13
![Second Choice “reject” Prof. Busch - LSU 14 Second Choice “reject” Prof. Busch - LSU 14](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-14.jpg)
Second Choice “reject” Prof. Busch - LSU 14
![Another Rejection example Prof. Busch - LSU 15 Another Rejection example Prof. Busch - LSU 15](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-15.jpg)
Another Rejection example Prof. Busch - LSU 15
![First Choice Prof. Busch - LSU 16 First Choice Prof. Busch - LSU 16](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-16.jpg)
First Choice Prof. Busch - LSU 16
![First Choice Input cannot be consumed “reject” Automaton halts Prof. Busch - LSU 17 First Choice Input cannot be consumed “reject” Automaton halts Prof. Busch - LSU 17](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-17.jpg)
First Choice Input cannot be consumed “reject” Automaton halts Prof. Busch - LSU 17
![Second Choice Prof. Busch - LSU 18 Second Choice Prof. Busch - LSU 18](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-18.jpg)
Second Choice Prof. Busch - LSU 18
![Second Choice Input cannot be consumed Automaton halts “reject” Prof. Busch - LSU 19 Second Choice Input cannot be consumed Automaton halts “reject” Prof. Busch - LSU 19](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-19.jpg)
Second Choice Input cannot be consumed Automaton halts “reject” Prof. Busch - LSU 19
![An NFA rejects a string: if there is no computation of the NFA that An NFA rejects a string: if there is no computation of the NFA that](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-20.jpg)
An NFA rejects a string: if 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 accepting state OR • The input cannot be consumed Prof. Busch - LSU 20
![is rejected by the NFA: “reject” All possible computations lead to rejection Prof. Busch is rejected by the NFA: “reject” All possible computations lead to rejection Prof. Busch](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-21.jpg)
is rejected by the NFA: “reject” All possible computations lead to rejection Prof. Busch - LSU 21
![is rejected by the NFA: “reject” All possible computations lead to rejection Prof. Busch is rejected by the NFA: “reject” All possible computations lead to rejection Prof. Busch](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-22.jpg)
is rejected by the NFA: “reject” All possible computations lead to rejection Prof. Busch - LSU 22
![Language accepted: Prof. Busch - LSU 23 Language accepted: Prof. Busch - LSU 23](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-23.jpg)
Language accepted: Prof. Busch - LSU 23
![Lambda Transitions Prof. Busch - LSU 24 Lambda Transitions Prof. Busch - LSU 24](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-24.jpg)
Lambda Transitions Prof. Busch - LSU 24
![Prof. Busch - LSU 25 Prof. Busch - LSU 25](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-25.jpg)
Prof. Busch - LSU 25
![Prof. Busch - LSU 26 Prof. Busch - LSU 26](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-26.jpg)
Prof. Busch - LSU 26
![input tape head does not move Automaton changes state Prof. Busch - LSU 27 input tape head does not move Automaton changes state Prof. Busch - LSU 27](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-27.jpg)
input tape head does not move Automaton changes state Prof. Busch - LSU 27
![all input is consumed “accept” String is accepted Prof. Busch - LSU 28 all input is consumed “accept” String is accepted Prof. Busch - LSU 28](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-28.jpg)
all input is consumed “accept” String is accepted Prof. Busch - LSU 28
![Rejection Example Prof. Busch - LSU 29 Rejection Example Prof. Busch - LSU 29](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-29.jpg)
Rejection Example Prof. Busch - LSU 29
![Prof. Busch - LSU 30 Prof. Busch - LSU 30](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-30.jpg)
Prof. Busch - LSU 30
![(read head doesn’t move) Prof. Busch - LSU 31 (read head doesn’t move) Prof. Busch - LSU 31](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-31.jpg)
(read head doesn’t move) Prof. Busch - LSU 31
![Input cannot be consumed Automaton halts “reject” String is rejected Prof. Busch - LSU Input cannot be consumed Automaton halts “reject” String is rejected Prof. Busch - LSU](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-32.jpg)
Input cannot be consumed Automaton halts “reject” String is rejected Prof. Busch - LSU 32
![Language accepted: Prof. Busch - LSU 33 Language accepted: Prof. Busch - LSU 33](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-33.jpg)
Language accepted: Prof. Busch - LSU 33
![Another NFA Example Prof. Busch - LSU 34 Another NFA Example Prof. Busch - LSU 34](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-34.jpg)
Another NFA Example Prof. Busch - LSU 34
![Prof. Busch - LSU 35 Prof. Busch - LSU 35](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-35.jpg)
Prof. Busch - LSU 35
![Prof. Busch - LSU 36 Prof. Busch - LSU 36](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-36.jpg)
Prof. Busch - LSU 36
![“accept” Prof. Busch - LSU 37 “accept” Prof. Busch - LSU 37](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-37.jpg)
“accept” Prof. Busch - LSU 37
![Another String Prof. Busch - LSU 38 Another String Prof. Busch - LSU 38](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-38.jpg)
Another String Prof. Busch - LSU 38
![Prof. Busch - LSU 39 Prof. Busch - LSU 39](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-39.jpg)
Prof. Busch - LSU 39
![Prof. Busch - LSU 40 Prof. Busch - LSU 40](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-40.jpg)
Prof. Busch - LSU 40
![Prof. Busch - LSU 41 Prof. Busch - LSU 41](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-41.jpg)
Prof. Busch - LSU 41
![Prof. Busch - LSU 42 Prof. Busch - LSU 42](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-42.jpg)
Prof. Busch - LSU 42
![Prof. Busch - LSU 43 Prof. Busch - LSU 43](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-43.jpg)
Prof. Busch - LSU 43
![“accept” Prof. Busch - LSU 44 “accept” Prof. Busch - LSU 44](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-44.jpg)
“accept” Prof. Busch - LSU 44
![Language accepted Prof. Busch - LSU 45 Language accepted Prof. Busch - LSU 45](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-45.jpg)
Language accepted Prof. Busch - LSU 45
![Another NFA Example Prof. Busch - LSU 46 Another NFA Example Prof. Busch - LSU 46](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-46.jpg)
Another NFA Example Prof. Busch - LSU 46
![Language accepted (redundant state) Prof. Busch - LSU 47 Language accepted (redundant state) Prof. Busch - LSU 47](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-47.jpg)
Language accepted (redundant state) Prof. Busch - LSU 47
![Remarks: • The symbol never appears on the input tape • Simple automata: Prof. Remarks: • The symbol never appears on the input tape • Simple automata: Prof.](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-48.jpg)
Remarks: • The symbol never appears on the input tape • Simple automata: Prof. Busch - LSU 48
![• NFAs are interesting because we can express languages easier than DFAs NFA • NFAs are interesting because we can express languages easier than DFAs NFA](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-49.jpg)
• NFAs are interesting because we can express languages easier than DFAs NFA DFA Prof. Busch - LSU 49
![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](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-50.jpg)
Formal Definition of NFAs Set of states, i. e. Input aplhabet, i. e. Transition function Initial state Accepting states Prof. Busch - LSU 50
![Transition Function resulting states with following one transition with symbol Prof. Busch - LSU Transition Function resulting states with following one transition with symbol Prof. Busch - LSU](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-51.jpg)
Transition Function resulting states with following one transition with symbol Prof. Busch - LSU 51
![Prof. Busch - LSU 52 Prof. Busch - LSU 52](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-52.jpg)
Prof. Busch - LSU 52
![Prof. Busch - LSU 53 Prof. Busch - LSU 53](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-53.jpg)
Prof. Busch - LSU 53
![Prof. Busch - LSU 54 Prof. Busch - LSU 54](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-54.jpg)
Prof. Busch - LSU 54
![Prof. Busch - LSU 55 Prof. Busch - LSU 55](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-55.jpg)
Prof. Busch - LSU 55
![Extended Transition Function Same with but applied on strings Prof. Busch - LSU 56 Extended Transition Function Same with but applied on strings Prof. Busch - LSU 56](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-56.jpg)
Extended Transition Function Same with but applied on strings Prof. Busch - LSU 56
![Prof. Busch - LSU 57 Prof. Busch - LSU 57](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-57.jpg)
Prof. Busch - LSU 57
![Prof. Busch - LSU 58 Prof. Busch - LSU 58](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-58.jpg)
Prof. Busch - LSU 58
![Special case: for any state Prof. Busch - LSU 59 Special case: for any state Prof. Busch - LSU 59](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-59.jpg)
Special case: for any state Prof. Busch - LSU 59
![In general : there is a walk from with label Prof. Busch - LSU In general : there is a walk from with label Prof. Busch - LSU](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-60.jpg)
In general : there is a walk from with label Prof. Busch - LSU to 60
![The Language of an NFA The language accepted by is: where (accepting state) and The Language of an NFA The language accepted by is: where (accepting state) and](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-61.jpg)
The Language of an NFA The language accepted by is: where (accepting state) and there is some Prof. Busch - LSU 61
![Prof. Busch - LSU 62 Prof. Busch - LSU 62](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-62.jpg)
Prof. Busch - LSU 62
![Prof. Busch - LSU 63 Prof. Busch - LSU 63](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-63.jpg)
Prof. Busch - LSU 63
![Prof. Busch - LSU 64 Prof. Busch - LSU 64](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-64.jpg)
Prof. Busch - LSU 64
![Prof. Busch - LSU 65 Prof. Busch - LSU 65](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-65.jpg)
Prof. Busch - LSU 65
![Prof. Busch - LSU 66 Prof. Busch - LSU 66](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-66.jpg)
Prof. Busch - LSU 66
![Prof. Busch - LSU 67 Prof. Busch - LSU 67](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-67.jpg)
Prof. Busch - LSU 67
![NFAs accept the Regular Languages Prof. Busch - LSU 68 NFAs accept the Regular Languages Prof. Busch - LSU 68](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-68.jpg)
NFAs accept the Regular Languages Prof. Busch - LSU 68
![Equivalence of Machines Definition: Machine is equivalent to machine if Prof. Busch - LSU Equivalence of Machines Definition: Machine is equivalent to machine if Prof. Busch - LSU](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-69.jpg)
Equivalence of Machines Definition: Machine is equivalent to machine if Prof. Busch - LSU 69
![Example of equivalent machines NFA DFA Prof. Busch - LSU 70 Example of equivalent machines NFA DFA Prof. Busch - LSU 70](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-70.jpg)
Example of equivalent machines NFA DFA Prof. Busch - LSU 70
![Theorem: Languages accepted by NFAs Regular Languages accepted by DFAs NFAs and DFAs have Theorem: Languages accepted by NFAs Regular Languages accepted by DFAs NFAs and DFAs have](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-71.jpg)
Theorem: Languages accepted by NFAs Regular Languages accepted by DFAs NFAs and DFAs have the same computation power, accept the same set of languages Prof. Busch - LSU 71
![Proof: we only need to show Languages accepted by NFAs Regular Languages AND Languages Proof: we only need to show Languages accepted by NFAs Regular Languages AND Languages](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-72.jpg)
Proof: we only need to show Languages accepted by NFAs Regular Languages AND Languages accepted by NFAs Regular Languages Prof. Busch - LSU 72
![Proof-Step 1 Languages accepted by NFAs Regular Languages Every DFA is trivially an NFA Proof-Step 1 Languages accepted by NFAs Regular Languages Every DFA is trivially an NFA](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-73.jpg)
Proof-Step 1 Languages accepted by NFAs Regular Languages Every DFA is trivially an NFA Any language accepted by a DFA is also accepted by an NFA Prof. Busch - LSU 73
![Proof-Step 2 Languages accepted by NFAs Regular Languages Any NFA can be converted to Proof-Step 2 Languages accepted by NFAs Regular Languages Any NFA can be converted to](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-74.jpg)
Proof-Step 2 Languages accepted by NFAs Regular Languages Any NFA can be converted to an equivalent DFA Any language accepted by an NFA is also accepted by a DFA Prof. Busch - LSU 74
![Conversion NFA to DFA NFA DFA Prof. Busch - LSU 75 Conversion NFA to DFA NFA DFA Prof. Busch - LSU 75](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-75.jpg)
Conversion NFA to DFA NFA DFA Prof. Busch - LSU 75
![NFA DFA Prof. Busch - LSU 76 NFA DFA Prof. Busch - LSU 76](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-76.jpg)
NFA DFA Prof. Busch - LSU 76
![empty set NFA DFA trap state Prof. Busch - LSU 77 empty set NFA DFA trap state Prof. Busch - LSU 77](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-77.jpg)
empty set NFA DFA trap state Prof. Busch - LSU 77
![NFA union DFA Prof. Busch - LSU 78 NFA union DFA Prof. Busch - LSU 78](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-78.jpg)
NFA union DFA Prof. Busch - LSU 78
![NFA union DFA Prof. Busch - LSU 79 NFA union DFA Prof. Busch - LSU 79](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-79.jpg)
NFA union DFA Prof. Busch - LSU 79
![NFA DFA trap state Prof. Busch - LSU 80 NFA DFA trap state Prof. Busch - LSU 80](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-80.jpg)
NFA DFA trap state Prof. Busch - LSU 80
![END OF CONSTRUCTION NFA DFA Prof. Busch - LSU 81 END OF CONSTRUCTION NFA DFA Prof. Busch - LSU 81](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-81.jpg)
END OF CONSTRUCTION NFA DFA Prof. Busch - LSU 81
![General Conversion Procedure Input: an NFA Output: an equivalent DFA with Prof. Busch - General Conversion Procedure Input: an NFA Output: an equivalent DFA with Prof. Busch -](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-82.jpg)
General Conversion Procedure Input: an NFA Output: an equivalent DFA with Prof. Busch - LSU 82
![The NFA has states The DFA has states from the power set Prof. Busch The NFA has states The DFA has states from the power set Prof. Busch](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-83.jpg)
The NFA has states The DFA has states from the power set Prof. Busch - LSU 83
![Conversion Procedure Steps step 1. Initial state of NFA: Initial state of DFA: Prof. Conversion Procedure Steps step 1. Initial state of NFA: Initial state of DFA: Prof.](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-84.jpg)
Conversion Procedure Steps step 1. Initial state of NFA: Initial state of DFA: Prof. Busch - LSU 84
![Example NFA DFA Prof. Busch - LSU 85 Example NFA DFA Prof. Busch - LSU 85](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-85.jpg)
Example NFA DFA Prof. Busch - LSU 85
![step 2. For every DFA’s state compute in the NFA Union add transition to step 2. For every DFA’s state compute in the NFA Union add transition to](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-86.jpg)
step 2. For every DFA’s state compute in the NFA Union add transition to DFA Prof. Busch - LSU 86
![Example NFA DFA Prof. Busch - LSU 87 Example NFA DFA Prof. Busch - LSU 87](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-87.jpg)
Example NFA DFA Prof. Busch - LSU 87
![step 3. Repeat Step 2 for every state in DFA and symbols in alphabet step 3. Repeat Step 2 for every state in DFA and symbols in alphabet](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-88.jpg)
step 3. Repeat Step 2 for every state in DFA and symbols in alphabet until no more states can be added in the DFA Prof. Busch - LSU 88
![Example NFA DFA Prof. Busch - LSU 89 Example NFA DFA Prof. Busch - LSU 89](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-89.jpg)
Example NFA DFA Prof. Busch - LSU 89
![step 4. For any DFA state if some is accepting state in NFA Then, step 4. For any DFA state if some is accepting state in NFA Then,](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-90.jpg)
step 4. For any DFA state if some is accepting state in NFA Then, is accepting state in DFA Prof. Busch - LSU 90
![Example NFA DFA Prof. Busch - LSU 91 Example NFA DFA Prof. Busch - LSU 91](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-91.jpg)
Example NFA DFA Prof. Busch - LSU 91
![Lemma: If we convert NFA to DFA then the two automata are equivalent: Proof: Lemma: If we convert NFA to DFA then the two automata are equivalent: Proof:](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-92.jpg)
Lemma: If we convert NFA to DFA then the two automata are equivalent: Proof: We only need to show: AND Prof. Busch - LSU 92
![First we show: We only need to prove: Prof. Busch - LSU 93 First we show: We only need to prove: Prof. Busch - LSU 93](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-93.jpg)
First we show: We only need to prove: Prof. Busch - LSU 93
![NFA Consider symbols Prof. Busch - LSU 94 NFA Consider symbols Prof. Busch - LSU 94](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-94.jpg)
NFA Consider symbols Prof. Busch - LSU 94
![symbol denotes a possible sub-path like symbol Prof. Busch - LSU 95 symbol denotes a possible sub-path like symbol Prof. Busch - LSU 95](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-95.jpg)
symbol denotes a possible sub-path like symbol Prof. Busch - LSU 95
![We will show that if NFA then DFA state label Prof. Busch - LSU We will show that if NFA then DFA state label Prof. Busch - LSU](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-96.jpg)
We will show that if NFA then DFA state label Prof. Busch - LSU 96
![More generally, we will show that if in : (arbitrary string) NFA then DFA More generally, we will show that if in : (arbitrary string) NFA then DFA](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-97.jpg)
More generally, we will show that if in : (arbitrary string) NFA then DFA Prof. Busch - LSU 97
![Proof by induction on Induction Basis: NFA DFA is true by construction of Prof. Proof by induction on Induction Basis: NFA DFA is true by construction of Prof.](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-98.jpg)
Proof by induction on Induction Basis: NFA DFA is true by construction of Prof. Busch - LSU 98
![Induction hypothesis: Suppose that the following hold NFA DFA Prof. Busch - LSU 99 Induction hypothesis: Suppose that the following hold NFA DFA Prof. Busch - LSU 99](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-99.jpg)
Induction hypothesis: Suppose that the following hold NFA DFA Prof. Busch - LSU 99
![Induction Step: Then this is true by construction of NFA DFA Prof. Busch - Induction Step: Then this is true by construction of NFA DFA Prof. Busch -](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-100.jpg)
Induction Step: Then this is true by construction of NFA DFA Prof. Busch - LSU 100
![Therefore if NFA then DFA Prof. Busch - LSU 101 Therefore if NFA then DFA Prof. Busch - LSU 101](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-101.jpg)
Therefore if NFA then DFA Prof. Busch - LSU 101
![We have shown: With a similar proof we can show: Therefore: END OF LEMMA We have shown: With a similar proof we can show: Therefore: END OF LEMMA](http://slidetodoc.com/presentation_image/9c431c8bd32a4a658c9a7d0484716083/image-102.jpg)
We have shown: With a similar proof we can show: Therefore: END OF LEMMA PROOF Prof. Busch - LSU 102
- Slides: 102