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PrasadL12NFA2DFA1 NFA to DFA Conversion Rabin and Scott (1959)

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PrasadL12NFA2DFA2 Removing Nondeterminism By simulating all moves of an NFA-λ in parallel using a DFA. λ-closure of a state is the set of states reachable using only the λ-transitions.

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PrasadL12NFA2DFA3 NFA-λ q1 p1 q2 p3 p2 a λ λ λ p4 a p5 λ

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PrasadL12NFA2DFA4

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PrasadL12NFA2DFA5 Transition Function

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PrasadL12NFA2DFA6

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PrasadL12NFA2DFA7 Equivalence Construction Given NFA-λ M, construct a DFA DM such that L (M) = L (DM). Observe that –A node of the DFA = Set of nodes of NFA-λ –Transition of the DFA = Transition among set of nodes of NFA- λ

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PrasadL12NFA2DFA8 {q1,…,qn}{p1,…,pm} a For every pi, there exists qj such that

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PrasadL12NFA2DFA9 Start state of DFA = Final/Accepting state of DFA = All subsets of states of NFA-λ that contain an accepting state of the NFA-λ Dead state of DFA =

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PrasadL12NFA2DFA10 Example q0 q1 q2 a a a b λ c a+c*b*

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PrasadL12NFA2DFA11 {q0} {q0,q1,q2} a b c

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PrasadL12NFA2DFA12 {q0} {q0,q1,q2} a b c {q1} {q1,q2} a b c a,b,c

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PrasadL12NFA2DFA13 {q1} a,c b {q1,q2} a c {q1} b

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PrasadL12NFA2DFA14 Equivalent DFA {q0} {q0,q1,q2} {q1} {q1,q2} a a a,c a a,b,c b b bb,c c c

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1 1 CDT314 FABER Formal Languages, Automata and Models of Computation Lecture 3 School of Innovation, Design and Engineering Mälardalen University 2012.

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