# NFAtoFA - Converting an NFA into an FSA Proving LNFA is a...

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Converting an NFA into an FSA Proving LNFA is a subset of LFSA.

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Purpose • This presentation presents an example execution of the algorithm which takes as input an NFA (without λ - transitions) and produces as output an equivalent FSA • Algorithm Specification – Input: NFA M 1 (without λ -transitions) – Output: FSA M 2 such that L(M 2 ) = L(M 1 )
Input NFA M 1 a b a,b b b aa 1 2 3 4 5 6

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Initialization a b a,b b b aa 1 2 3 4 5 6 ab {1} Initial State of FSA M 2 : {1}
Expand State {1} a b a,b b b aa 1 2 3 4 5 6 a b {1} {2} {3}

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Add States {2} and {3} a b a,b b b aa 1 2 3 4 5 6 a b {1} {2} {3} {2} {3}
Expand State {2} a b a,b b b aa 1 2 3 4 5 6 a b {1} {2} {3} {2} {} {} {3}

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Add State {} a b a,b b b aa 1 2 3 4 5 6 a b {1} {2} {3} {2} {} {} {3} {}
Expand State {3} a b a,b b b aa 1 2 3 4 5 6 ab {1} {2} {3} {2} {} {} {3} {3,4} {3,5} {}

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Add States {3,4} and {3,5} a b a,b b b aa 1 2 3 4 5 6 a b {1} {2} {3} {2} {} {} {3} {3,4} {3,5} {} {3,4} {3,5}
Expand State {} a b a,b b b aa 1 2 3 4 5 6 a b {1} {2} {3} {2} {} {} {3} {3,4} {3,5} {} {} {} {3,4} {3,5}

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No New States Added a b a,b b b aa 1 2 3 4 5 6 a b {1} {2} {3} {2} {} {} {3} {3,4} {3,5} {} {} {} {3,4} {3,5}
Expand State {3,4} a b a,b b b aa 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}

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## This note was uploaded on 07/25/2008 for the course CSE 460 taught by Professor Torng during the Fall '07 term at Michigan State University.

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NFAtoFA - Converting an NFA into an FSA Proving LNFA is a...

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