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NtoFIntuition

# NtoFIntuition - Converting an NFA into an FSA Why the...

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Why the algorithm works! Converting an NFA into an FSA

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Purpose This presentation attempts to give the reader some intuition as to why the algorithm which takes as input an NFA without λ -transitions and produces as output an equivalent FSA works correctly . We use the example from the previous presentation to illustrate this intuition.
Why the Construction Works a b a,b b b a a 1 2 3 4 5 6 a b { 1 } {2} {3} {2} {} {} {3} {3,4} {3,5} {} {} {} {3,4} {3,4,6} {3,5} {3,5} {3,4} {3,5,6} { 3,4,6 } {3,4,6} {3,5} { 3,5,6 } {3,4} {3,5,6} NFA Equivalent FSA Input String babaa

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Key Idea a b a,b b b a a 1 2 3 4 5 6 a b { 1 } {2} {3} {2} {} {} {3} {3,4} {3,5} {} {} {} {3,4} {3,4,6} {3,5} {3,5} {3,4} {3,5,6} { 3,4,6 } {3,4,6} {3,5} { 3,5,6 } {3,4} {3,5,6} NFA Equivalent FSA We will illustrate the computation of both the NFA and the FSA on the input string babaa . In all configurations, the set of states the NFA is in will be identical to the state the FSA is in.
Initial Configurations a b a,b b b a a 1 2 3 4 5 6 a b {1} {2} {3} {2} {} {} {3} {3,4} {3,5} {} {} {} {3,4} {3,4,6} {3,5} {3,5} {3,4} {3,5,6} {3,4,6} {3,4,6} {3,5} {3,5,6} {3,4} {3,5,6} ( 1 , babaa) ( {1} , babaa)

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Second Configurations a b a,b b b a a 1 2 3 4 5 6 a b {1} {2} {3} {2} {} {} {3} {3,4} {3,5} {} {} {} {3,4} {3,4,6} {3,5} {3,5} {3,4} {3,5,6} {3,4,6} {3,4,6} {3,5} {3,5,6} {3,4} {3,5,6} (1, babaa) ({1}, babaa) ( 3 , abaa) ( {3} , abaa)
Third Configurations a b a,b b b a a 1 2 3 4 5 6 a b {1} {2} {3} {2} {} {} {3} {3,4} {3,5} {} {} {} {3,4} {3,4,6} {3,5} {3,5} {3,4} {3,5,6} {3,4,6} {3,4,6} {3,5}

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