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1 Non-Deterministic Finite Automata
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2 Alphabet = Nondeterministic Finite Automaton (NFA)
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3 Two choices Alphabet =
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4 No transition Two choices No transition Alphabet =
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5 First Choice
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8 “accept” First Choice All input is consumed
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9 Second Choice
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10 Second Choice
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11 Second Choice No transition: the automaton hangs
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12 Second Choice “reject” Input cannot be consumed
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13 An NFA accepts a string: when there is a computation of the NFA that accepts the string all the input is consumed and the automaton is in an accepting state There is a computation:
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14 Example is accepted by the NFA: “accept” “reject” because this computation accepts
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15 Rejection example
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16 First Choice
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17 First Choice “reject”
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18 Second Choice
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19 Second Choice
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20 Second Choice “reject”
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21 An NFA rejects a string: when there is no computation of the NFA that accepts the string. All the input is consumed and the automaton is in a non final state The input cannot be consumed OR For each computation:
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22 Example is rejected by the NFA: “reject” All possible computations lead to rejection
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23 Rejection example
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24 First Choice
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25 First Choice No transition: the automaton hangs
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26 “reject” First Choice Input cannot be consumed
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27 Second Choice
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28 Second Choice
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29 Second Choice No transition: the automaton hangs
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30 Second Choice “reject” Input cannot be consumed
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31 is rejected by the NFA: “reject” All possible computations lead to rejection
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32 Language accepted:
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33 Lambda Transitions
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36 (read head does not move)
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38 “accept” String is accepted all input is consumed
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39 Rejection Example
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41 (read head doesn’t move)
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42 No transition: the automaton hangs
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43 “reject” String is rejected Input cannot be consumed
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44 Language accepted:
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45 Another NFA Example
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49 “accept”
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50 Another String
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57 “accept”
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58 Language accepted
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59 Another NFA Example
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60 Language accepted (redundant state)
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61 Remarks: The symbol never appears on the input tape Simple automata:
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62 NFA FA NFAs are interesting because we can express languages easier than FAs
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63 Formal Definition of NFAs Set of states, i.e. Input aplhabet, i.e. Transition function Initial state Accepting states
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64 Transition Function
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68 Extended Transition Function
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71 Formally : there is a walk from to with label
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72 The Language of an NFA
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77 Formally The language accepted by NFA is: where and there is some (accepting state)
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