NFA - NonDeterministic FiniteAutomata...

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Non-Deterministic  Finite Automata
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1 q 2 q 3 q a a a 0 q } { a Alphabet = Nondeterministic Finite Automaton  (NFA)
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1 q 2 q 3 q a a a 0 q Two choices } { a Alphabet =
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No transition 1 q 2 q 3 q a a a 0 q Two choices No transition } { a Alphabet =
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a a 0 q 1 q 2 q 3 q a a First Choice a
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a a 0 q 1 q 2 q 3 q a a a First Choice
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a a 0 q 1 q 2 q 3 q a a a “accept” First Choice All input is consumed
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a a 0 q 1 q 2 q 3 q a a Second Choice a
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a a 0 q 1 q 2 q a a a 3 q Second Choice “reject” Input cannot be consumed Automaton Halts
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An NFA accepts a string: if the re  is  a c o m puta tio n o f the  NFA tha t a c c e pts  the  s tring   i.e., all the input string is processed and the  automaton is in an accepting state
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aa is accepted by the NFA: 0 q 1 q 2 q 3 q a a a “accept” 0 q 1 q 2 q a a a 3 q “reject” because this  computation accepts  aa this computation is ignored
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a 0 q 1 q 2 q 3 q a a Rejection example a
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a 0 q 1 q 2 q 3 q a a a First Choice “reject”
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Second Choice a 0 q 1 q 2 q 3 q a a a
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Second Choice a 0 q 1 q 2 q a a a 3 q “reject”
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Another Rejection example a a 0 q 1 q 2 q 3 q a a a a
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a a 0 q 1 q 2 q 3 q a a a First Choice a
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a a 0 q 1 q 2 q 3 q a a a “reject” First Choice a Input cannot be consumed Automaton halts
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a a 0 q 1 q 2 q 3 q a a Second Choice a a
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a a 0 q 1 q 2 q a a a 3 q Second Choice “reject” a Input cannot be consumed Automaton halts
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An NFA rejects a string: if the re   is  no  c o m putatio n o f the  NFA tha t a c c e pts  the  s tring .   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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a is rejected by the NFA: 0 q 1 q 2 q a a a 3 q “reject” 0 q 1 q 2 q a a a 3 q “reject” All possible computations lead to rejection
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aaa is rejected by the NFA: 0 q 1 q 2 q 3 q a a a “reject” 0 q 1 q 2 q a a a 3 q “reject” All possible computations lead to rejection
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1 q 2 q 3 q a a a 0 q Language accepted: } { aa L =
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Lambda Transitions 1 q 3 q a 0 q λ 2 q a
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a a 1 q 3 q a 0 q λ 2 q a
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a a 1 q 3 q a 0 q λ 2 q a
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a a 1 q 3 q a 0 q λ 2 q a input tape head does not move
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a a 1 q 3 q a 0 q λ 2 q a “accept” String        is accepted aa all input is consumed
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a a 1 q 3 q a 0 q λ 2 q a Rejection Example a
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This note was uploaded on 12/02/2011 for the course AR 107 taught by Professor Gracegraham during the Fall '11 term at Montgomery College.

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NFA - NonDeterministic FiniteAutomata...

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