(11+010)*(111)+(11+010)*(111)+

Machine to AcceptMachine to Accept

Initial Design

11

1

1 1

1

00

λ

λA

B

C

E

D

F

G

H

State Table0 1 λ

->

A B C D

B E

C A

D F

E A

F G

G H

H D *

Nothing to do in this example

Complete Nulls

Remove nulls0 1 λ

->

A B C D

B E

C A

D F

E A

F G

G H

H D *

0 1

-> A B CF

B E

C A

D F

E A

F G

G H

H F *

Convert to deterministic0 1

-> A B CF

B E

C A

D F

E A

F G

G H

H F *

0 1

-> A B CF

B E

CF AG

E A

AG B CFH

CFH AFG *

AFG B CFGH

CFGH AFGH *

AFGH B CFGH *

Rename0 1

-> a b c

b d e

c d f

d d d

e a d

f b g

g d h *

h b i

i d j *

j b i *

0 1

-> A B CF

B E

CF AG

E A

AG B CFH

CFH AFG *

AFG B CFGH

CFGH AFGH *

AFGH B CFGH *

0 & 1 - equivalence

0 1 =0

0 1 =1

-> a b c 0 0 0 0

b d e 0 0 0 0

c d f 0 0 0 0

d d d 0 0 0 0

e a d 0 0 0 0

f b g 0 0 1 1

g d h 1 0 0 2

h b i 0 0 1 1

i d j 1 0 1 3

j b i 1 0 1 3

1 & 2 -equivalence

0 1 =1

0 1 =2

-> a b c 0 0 0 0

b d e 0 0 0 0

c d f 0 0 1 1

d d d 0 0 0 0

e a d 0 0 0 0

f b g 1 0 2 2

g d h 2 0 1 3

h b i 1 0 3 4

i d j 3 0 3 5

j b i 3 0 3 5

2 & 3 - equivalence

0 1 =2

0 1 =3

-> a b c 0 0 1 0

b d e 0 0 0 1

c d f 1 0 2 2

d d d 0 0 0 1

e a d 0 0 0 1

f b g 2 0 3 3

g d h 3 0 4 4

h b i 4 0 5 5

i d j 5 0 5 6

j b i 5 0 5 6

3 & 4 - equivalence0 1 =

30 1 =

4

-> a b c 0 1 2 0

b d e 1 1 1 1

c d f 2 1 3 2

d d d 1 1 1 1

e a d 1 0 1 4

f b g 3 1 4 5

g d h 4 1 5 6

h b i 5 1 6 7

i d j 6 1 6 8

j b i 6 1 6 8

4 & 5 - equivalence0 1 =

40 1 =

5

-> a b c 0 1 2 0

b d e 1 3 4 1

c d f 2 3 5 2

d d d 1 3 3 3

e a d 4 0 3 4

f b g 5 1 6 5

g d h 6 3 7 6

h b i 7 1 8 7

i d j 8 3 8 8

j b i 8 1 8 9

5 & 6 - equivalence

0 1 =5

0 1 =6

-> a b c 0 1 2 0

b d e 1 3 4 1

c d f 2 3 5 2

d d d 3 3 3 3

e a d 4 0 3 4

f b g 5 1 6 5

g d h 6 3 7 6

h b i 7 1 8 7

i d j 8 3 9 8

j b i 9 1 8 9

Minimized machineState 0 1

-> 0 1 2

1 3 4

2 3 5

3 3 3

4 0 3

5 1 6

6 3 7 *

7 1 8

8 3 9 *

9 1 8 *

0

2 5

6

7

8

9

1

11

1

1

1

1

1

41

00

0

0

0

Our machine for

(11+010)*(111)+

3 black hole