Why the algorithm works! Converting an NFA into an FSA.

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Presentation transcript:

Why the algorithm works! Converting an NFA into an FSA

Purpose This presentation attempts to give the reader some intuition as to why the algorithm which takes as input an NFA without -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 aa NFAEquivalent FSA Input String babaa

Key Idea a b a,b b b aa NFAEquivalent 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 aa (1,[1,babaa]) ({1},[1,babaa])

Second Configurations a b a,b b b aa (1,[1,babaa]) ({1},[1,babaa]) (3,[2,babaa])({3},[2,babaa])

Third Configurations a b a,b b b aa (1,[1,babaa]) ({1},[1,babaa]) (3,[2,babaa])({3},[2,babaa]) (3,[3,babaa])(4,[3,babaa])({3,4}, [3,babaa])

Fourth Configurations a b a,b b b aa (1,[1,babaa]) ({1},[1,babaa]) (3,[2,babaa])({3},[2,babaa]) (3,[3,babaa])(4,[3,babaa])({3,4}, [3,babaa]) (3,[4,babaa]) (5,[4,babaa]) ({3,5}, [4,babaa])

Fifth Configurations a b a,b b b aa (1,[1,babaa]) ({1},[1,babaa]) (3,[2,babaa])({3},[2,babaa]) (3,[3,babaa])(4,[3,babaa])({3,4}, [3,babaa]) (3,[4,babaa]) (5,[4,babaa]) ({3,5}, [4,babaa]) (3,[5,babaa])(4,[5,babaa]) ({3,4}, [5,babaa])

Final Configurations a b a,b b b aa (1,[1,babaa]) ({1},[1,babaa]) (3,[2,babaa])({3},[2,babaa]) (3,[3,babaa])(4,[3,babaa])({3,4}, [3,babaa]) (3,[4,babaa]) (5,[4,babaa]) ({3,5}, [4,babaa]) (3,[5,babaa])(4,[5,babaa]) ({3,4}, [5,babaa]) (3,[6,babaa])(4,[6,babaa])(6,[6,babaa]) ({3,4,6}, [6,babaa])