NFA to DFA Conversion

1
NFA to DFA Conversion

• Rabin and Scott (1959)

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Removing Nondeterminism

• By simulating all moves of an NFA-? in parallel
  using a DFA.
• ?-closure of a state is the set of states
  reachable using only the ?-transitions.

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NFA-?
p2
?
p1
a
p3
q1
?
?
p5
?
q2
a
p4
4
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Transition Function
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Equivalence Construction

• Given NFA-? M, construct a DFA DM such that L(M)
  L(DM).
• Observe that
• A node of the DFA Set of nodes of NFA-?
• Transition of the DFA Transition among set of
  nodes of NFA- ?

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q1,,qn
p1,,pm
a
For every pi, there exists qj such that
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Start state of DFA
Final/Accepting state of DFA All subsets of
states of NFA-? that contain an accepting state
of the NFA-?
Dead state of DFA
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Example
a
b
q1
a
q0
acb
?
a
q2
c
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q0,q1,q2
a
b
c
f
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a
b
q1
c
q1,q2
a,b,c
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c
q1
b
q1,q2
a
f
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Equivalent DFA
a
a
q0
q0,q1,q2
c
c
q1,q2
b
b
b,c
b
a,c
q1
f
a
a,b,c