Download - Finite Automaton: Example 1
CMSC 330 - Spring 2011 1
Finite Automaton: Example 1
0 0 1 0 1 1accepted
CMSC 330 - Spring 2011 2
Finite Automaton: Example 2
0 0 1 0 1 0not accepted
Reducing REs to NFAs
CMSC 330 - Spring 2011 3
ab
b
ε
a
b
✓
NFA for (ab|ba)*
CMSC 330 - Spring 2011 4
(ab|ba)*
b(ab|ba)* a(ab|ba)*
a b
✓
b a
NFA for (ab|aba)*
CMSC 330 - Spring 2011 5
(ab|aba)*
b(ab|aba)* ba(ab|aba)*
a a
✓
b
a
a(ab|aba)*
b
6
NFA DFA Example 1
• r0 = {S1}
• R = {r0} = { {S1} }
• r R = {S1}
• move({S1}, a} = {S2,S3} R = R ∪ {{S2,S3}} = { {S1}, {S2,S3} } = ∪ {<{S1}, a, {S2,S3}>}
• move({S1},b} = Ø R = R ∪ {Ø}
= { Ø, {S1}, {S2,S3} } = ∪ {<{S1}, b, Ø>}
bS1 S2 S3
a
a
a{S2,S3}{S1}
NFA
DFA
∅
b
7
NFA DFA Example 1 (cont.)
• R = { {S1}, {S2,S3}, Ø }
• r R = {S2,S3}
• move({S2,S3},a} = Ø
• move({S2,S3},b} = {S3} R = R ∪ {{S3} = { {S1}, {S2,S3} }, Ø, {S3} } = ∪ {<{S2,S3},a, Ø >, <{S2,S3}, b, {S3}>}
bS1 S2 S3
a
a
a b{S3}{S1}
NFA
DFA
∅
b{S2,S3}
a
8
NFA DFA Example 1 (cont.)
• R = { {S1}, {S2,S3}, Ø, {S3} }
• r R = Ø
• move(Ø,a} = Ø
• move(Ø,b} = Ø R = { {S1}, {S2,S3} }, Ø, {S3} } = ∪ {< Ø,a,Ø >, <Ø,b, Ø>}
bS1 S2 S3
a
a
a b{S1}
NFA
DFA
∅
b{S2,S3}
a
a b
{S3}
9
NFA DFA Example 1 (cont.)
• R = { {S1}, {S2,S3}, Ø, {S3} }
• r R = {S3}
• move({S3},a} = Ø
• move({S3},b} = Ø R = { {S1}, {S2,S3} }, Ø, {S3} } = ∪ {<{S3},a, Ø >, <{S3}, b, Ø>}
• Fd = {{S2,S3}, {S3}} Since S3 Fn
• Done!
bS1 S2 S3
a
a
NFA
DFA
a b{S1}
∅
b{S2,S3}
a
a b
{S3}
a,b
