1. Non-Deterministic Finite Automata
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2. Alphabet =
Two choices
No transition
No transition
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3. 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
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4. is accepted by the NFA: “accept” “reject” because this computation
accepts
this computation
is ignored
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5. Rejection example
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6. Another Rejection example
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7. OR 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
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8. Language accepted:
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9. Lambda Transitions
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10. Language accepted:
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11. Another NFA Example
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12. Language accepted
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13. Formal Definition of NFAs
Set of states, i.e.
Input aplhabet, i.e.
Transition function
Initial state
Accepting states
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16. Prof. Busch - LSU

17. In general
: there is a walk from to
with label
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18. The Language of an NFA The language accepted by is: where
and there is some
(accepting state)
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19. Prof. Busch - LSU

20. Equivalence of Machines
Definition:
Machine is equivalent to machine if
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21. Example of equivalent machines
NFA
DFA
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22. Theorem: Languages accepted Regular by NFAs Languages Languages
by DFAs
NFAs and DFAs have the same computation power,
accept the same set of languages
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23. Every DFA is trivially an NFA
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
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24. Any NFA can be converted to an equivalent DFA
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
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25. Conversion NFA to DFA
NFA
DFA
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26. NFA
DFA
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27. END OF CONSTRUCTION
NFA
DFA
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