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Non Deterministic Automata
Fall 2004 COMP 335
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Nondeterministic Finite Accepter (NFA)
Alphabet = Fall 2004 COMP 335
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Nondeterministic Finite Accepter (NFA)
Alphabet = Two choices Fall 2004 COMP 335
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Nondeterministic Finite Accepter (NFA)
Alphabet = Two choices No transition No transition Fall 2004 COMP 335
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First Choice Fall 2004 COMP 335
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First Choice Fall 2004 COMP 335
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First Choice Fall 2004 COMP 335
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First Choice All input is consumed “accept” Fall 2004 COMP 335
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Second Choice Fall 2004 COMP 335
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Second Choice Fall 2004 COMP 335
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Second Choice No transition: the automaton hangs Fall 2004 COMP 335
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Second Choice Input cannot be consumed “reject” Fall 2004 COMP 335
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AND An NFA accepts a string w:
if there is at least one computation of the NFA that accepts the string w AND all the input is consumed and the automaton is in a final state Fall 2004 COMP 335
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Example is accepted by the NFA: “accept” “reject” because this
computation accepts Fall 2004 COMP 335
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Rejection example Fall 2004 COMP 335
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First Choice Fall 2004 COMP 335
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First Choice “reject” Fall 2004 COMP 335
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Second Choice Fall 2004 COMP 335
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Second Choice Fall 2004 COMP 335
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Second Choice “reject” Fall 2004 COMP 335
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OR An NFA rejects a string w: if there is no computation of the NFA
that accepts the string w: All the input is consumed and the automaton is in a non final state OR The input cannot be consumed Fall 2004 COMP 335
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Example is rejected by the NFA: “reject” “reject”
All possible computations lead to rejection Fall 2004 COMP 335
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Rejection example Fall 2004 COMP 335
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First Choice Fall 2004 COMP 335
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First Choice No transition: the automaton hangs Fall 2004 COMP 335
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First Choice Input cannot be consumed “reject” Fall 2004 COMP 335
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Second Choice Fall 2004 COMP 335
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Second Choice Fall 2004 COMP 335
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Second Choice No transition: the automaton hangs Fall 2004 COMP 335
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Second Choice Input cannot be consumed “reject” Fall 2004 COMP 335
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All possible computations lead to rejection
is rejected by the NFA: “reject” “reject” All possible computations lead to rejection Fall 2004 COMP 335
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Language accepted: Fall 2004 COMP 335
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Lambda Transitions Fall 2004 COMP 335
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Fall 2004 COMP 335
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Fall 2004 COMP 335
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(read head does not move)
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Fall 2004 COMP 335
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all input is consumed “accept” String is accepted Fall 2004 COMP 335
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Rejection Example Fall 2004 COMP 335
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Fall 2004 COMP 335
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(read head doesn’t move)
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No transition: the automaton hangs Fall 2004 COMP 335
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Input cannot be consumed
“reject” String is rejected Fall 2004 COMP 335
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Language accepted: Fall 2004 COMP 335
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Another NFA Example Fall 2004 COMP 335
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Fall 2004 COMP 335
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Fall 2004 COMP 335
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Fall 2004 COMP 335
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“accept” Fall 2004 COMP 335
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Another String Fall 2004 COMP 335
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Fall 2004 COMP 335
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Fall 2004 COMP 335
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Fall 2004 COMP 335
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Fall 2004 COMP 335
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Fall 2004 COMP 335
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Fall 2004 COMP 335
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“accept” Fall 2004 COMP 335
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Language accepted Fall 2004 COMP 335
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