Non-Deterministic Finite Automata Prof. Busch - LSU

Alphabet = Two choices No transition No transition Prof. Busch - LSU

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

is accepted by the NFA: “accept” “reject” because this computation accepts this computation is ignored Prof. Busch - LSU

Rejection example Prof. Busch - LSU

Another Rejection example Prof. Busch - LSU

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 Prof. Busch - LSU

Language accepted: Prof. Busch - LSU

Lambda Transitions Prof. Busch - LSU

Language accepted: Prof. Busch - LSU

Another NFA Example Prof. Busch - LSU

Language accepted Prof. Busch - LSU

Formal Definition of NFAs Set of states, i.e. Input aplhabet, i.e. Transition function Initial state Accepting states Prof. Busch - LSU

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In general : there is a walk from to with label Prof. Busch - LSU

The Language of an NFA The language accepted by is: where and there is some (accepting state) Prof. Busch - LSU

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Equivalence of Machines Definition: Machine is equivalent to machine if Prof. Busch - LSU

Example of equivalent machines NFA DFA Prof. Busch - LSU

Theorem: Languages accepted Regular by NFAs Languages Languages by DFAs NFAs and DFAs have the same computation power, accept the same set of languages Prof. Busch - LSU

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 Prof. Busch - LSU

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 Prof. Busch - LSU

Conversion NFA to DFA NFA DFA Prof. Busch - LSU

NFA DFA Prof. Busch - LSU

END OF CONSTRUCTION NFA DFA Prof. Busch - LSU