Finite-State Machines

2

Transition assigned machine (Mealy)

1/1

B

D

CA

0/00/1 0/1

0/01/1

1/0 1/0

3

State assigned machine (Moore)

B, 1

D, 3

C, 2A, 0

1

1

1

1

0 0

00

D B 0

A C 1

B D 2

C A 3

A

B

C

D

0 1

(a) State Diagram (b) State Table

4

Construction of Ms from Mt

0/1

BA

0/01/1

1/0

Ms :Mt :0

(A, 0), 0 (B, 0), 0

(A, 1), 1 (B, 1), 1

00

1

1

1

1

0

5

Example of the partitioning procedure

A

B

C

D

0 1

E

F

G

H

J

B, 0 C, 0

C, 1 D, 1

D, 0 E, 0

C, 1 B, 1

F, 1 E, 1

G, 0 C, 0

F, 1 G, 1

J, 1 B, 0

H, 1 D, 0

M:

P1: {A, C, F}, {B, D, E, G}, {H, J}

P2: {A, F}, {C}, {B, D, E, G}, {H, J}

P3: {A, F}, {C}, {B, D}, {E, G}, {H, J}

P4: {A}, {F}, {C}, {B, D}, {E, G}, {H, J}

00

00

11

6

Construction of a reduced machine

NewNamesin M

{A}P4:

'

{F} {C} {B, D} {E, G} {H, J}

U V W X Y Z

(a)

(b)

{B}, 0 {C}, 0

{G}, 0 {C}, 0

{D}, 0 {E}, 0

{C}, 1 {D, B}, 1

{F}, 1 {E, C}, 1

{J, H}, 1 {B, D}, 0

U {A}

V {F}

W {C}

X {B, D}

Y {E, G}

Z {H, J}

0 1New

Names Blocks

7

Testing two machines for equivalence

A

B

C

0 1

B, 0 A, 0

A, 0 C, 1

C, 1 A, 0

0 1

D

E

F

G

H

E, 0 D, 0

D, 0 F, 1

F, 1 D, 0

E, 0 H, 1

D, 1 G, 0D

E

F

G

H

E, 0 D, 0

D, 0 F, 1

F, 1 D, 0

E, 0 H, 1

D, 1 G, 0

A

B

C

0 1

B, 0 A, 0

A, 0 C, 1

C, 1 A, 0

M1

M2

(a) M1 (b) M2 (c) Sum of M1 and M2

P1 : {A, D}, {B, E, G}, {C, F, H}

P2 : {A, D}, {B, E}, {G}, {C, F}, {H}

P3 = P2