turing machine read/write – move left/right bb read/write head 001000 state qi

Turing MachineRead/Write – Move Left/Right

B B

Read/Write Head

0 0 1 0 0 0

State Qi

State Diagram for Modulus 3shows only the tape input

Q0

Q1

Q2

Start 1

1

00

1

0

Q3 Q4

BB

B

B,0,1

Turing MachineProgram To Compute Values

Modulus 3State, Write, Direction

State B 0 1

Q0 3,0,L, 0,B,R 1,B,R

Q1 3,1,L 2,B,R 0,B,R

Q2 4,0,L 1,B,R 2,B,R

Q3 Halt Halt Halt

Q4 3,1,L 3,1,L 3,1,L

Modulus 353 % 3

B B1 1 0 1 0 1

State Q0

State B 0 1

Q0 3,0,L, 0,B,R 1,B,R

Q1 3,1,L 2,B,R 0,B,R

Q2 4,0,L 1,B,R 2,B,R

Q3 Halt Halt Halt

Q4 3,1,L 3,1,L 3,1,L

New State – Write B

Modulus 353 % 3

B BB 1 0 1 0 1

State Q1

State B 0 1

Q0 3,0,L, 0,B,R 1,B,R

Q1 3,1,L 2,B,R 0,B,R

Q2 4,0,L 1,B,R 2,B,R

Q3 Halt Halt Halt

Q4 3,1,L 3,1,L 3,1,L

Modulus 353 % 3

B BB B 0 1 0 1

State Q0

State B 0 1

Q0 3,0,L, 0,B,R 1,B,R

Q1 3,1,L 2,B,R 0,B,R

Q2 4,0,L 1,B,R 2,B,R

Q3 Halt Halt Halt

Q4 3,1,L 3,1,L 3,1,L

Write B

Modulus 353 % 3

B BB B B 1 0 1

State Q0

State B 0 1

Q0 3,0,L, 0,B,R 1,B,R

Q1 3,1,L 2,B,R 0,B,R

Q2 4,0,L 1,B,R 2,B,R

Q3 Halt Halt Halt

Q4 3,1,L 3,1,L 3,1,L New State – Write B

Modulus 353 % 3

B BB B B B 0 1

State Q1

State B 0 1

Q0 3,0,L, 0,B,R 1,B,R

Q1 3,1,L 2,B,R 0,B,R

Q2 4,0,L 1,B,R 2,B,R

Q3 Halt Halt Halt

Q4 3,1,L 3,1,L 3,1,LNew State – Write B

Modulus 353 % 3

B BB B B B B 1

State Q2

State B 0 1

Q0 3,0,L, 0,B,R 1,B,R

Q1 3,1,L 2,B,R 0,B,R

Q2 4,0,L 1,B,R 2,B,R

Q3 Halt Halt Halt

Q4 3,1,L 3,1,L 3,1,LWrite B

Modulus 353 % 3

B BB B B B B B

State Q2

State B 0 1

Q0 3,0,L, 0,B,R 1,B,R

Q1 3,1,L 2,B,R 0,B,R

Q2 4,0,L 1,B,R 2,B,R

Q3 Halt Halt Halt

Q4 3,1,L 3,1,L 3,1,L

New State – Write 0

Modulus 353 % 3

B 0B B B B B B

State Q4

State B 0 1

Q0 3,0,L, 0,B,R 1,B,R

Q1 3,1,L 2,B,R 0,B,R

Q2 4,0,L 1,B,R 2,B,R

Q3 Halt Halt Halt

Q4 3,1,L 3,1,L 3,1,L

New State – Write 1

Modulus 353 % 3

B 0B B B B B 1

Q3 Halt

State B 0 1

Q0 3,0,L, 0,B,R 1,B,R

Q1 3,1,L 2,B,R 0,B,R

Q2 4,0,L 1,B,R 2,B,R

Q3 Halt Halt Halt

Q4 3,1,L 3,1,L 3,1,L

Turing MachineProgram To Add Unary Numbers

State, Write, Direction

State B 0 1

Q0 Halt 1,B,R 0,1,R

Q1 2,B,L Halt 1,1,R

Q2 Halt Halt 3,B,L

Q3 3,1,Halt Halt 3,1,L

Adding Two Unary Numbers2 + 3 = 5

B B1 1 0 1 1 1

State Q0

State B 0 1

Q0 Halt 1,B,R 0,1,R

Q1 2,B,L Halt 1,1,R

Q2 Halt Halt 3,B,L

Q3 - 1,Halt Halt 3,1,L

Adding Two Unary numbers 2 + 3 = 5

B B1 1 0 1 1 1

State Q0

State B 0 1

Q0 Halt 1,B,R 0,1,R

Q1 2,B,L Halt 1,1,R

Q2 Halt Halt 3,B,L

Q3 - 1,Halt Halt 3,1,L

Adding Two Unary numbers 2 + 3 = 5

B B1 1 0 1 1 1

State Q0 New State – Write B

State B 0 1

Q0 Halt 1,B,R 0,1,R

Q1 2,B,L Halt 1,1,R

Q2 Halt Halt 3,B,L

Q3 - 1,Halt Halt 3,1,L

Adding Two Unary numbers 2 + 3 = 5

B B1 1 B 1 1 1

State Q1

State B 0 1

Q0 Halt 1,B,R 0,1,R

Q1 2,B,L Halt 1,1,R

Q2 Halt Halt 3,B,L

Q3 - 1,Halt Halt 3,1,L

Adding Two Unary numbers 2 + 3 = 5

B B1 1 B 1 1 1

State Q1

State B 0 1

Q0 Halt 1,B,R 0,1,R

Q1 2,B,L Halt 1,1,R

Q2 Halt Halt 3,B,L

Q3 - 1,Halt Halt 3,1,L

Adding Two Unary numbers 2 + 3 = 5

B B1 1 B 1 1 1

State Q1

State B 0 1

Q0 Halt 1,B,R 0,1,R

Q1 2,B,L Halt 1,1,R

Q2 Halt Halt 3,B,L

Q3 - 1,Halt Halt 3,1,L

Adding Two Unary numbers 2 + 3 = 5

B B1 1 B 1 1 1

State Q1New State

State B 0 1

Q0 Halt 1,B,R 0,1,R

Q1 2,B,L Halt 1,1,R

Q2 Halt Halt 3,B,L

Q3 - 1,Halt Halt 3,1,L

Adding Two Unary numbers 2 + 3 = 5

B B1 1 B 1 1 1

State Q2

New State – Write B

State B 0 1

Q0 Halt 1,B,R 0,1,R

Q1 2,B,L Halt 1,1,R

Q2 Halt Halt 3,B,L

Q3 - 1,Halt Halt 3,1,L

Adding Two Unary numbers 2 + 3 = 5

B B1 1 B 1 1 B

State Q3

State B 0 1

Q0 Halt 1,B,R 0,1,R

Q1 2,B,L Halt 1,1,R

Q2 Halt Halt 3,B,L

Q3 - 1,Halt Halt 3,1,L

Adding Two Unary numbers 2 + 3 = 5

B B1 1 B 1 1 B

State Q3

State B 0 1

Q0 Halt 1,B,R 0,1,R

Q1 2,B,L Halt 1,1,R

Q2 Halt Halt 3,B,L

Q3 - 1,Halt Halt 3,1,L

Adding Two Unary numbers 2 + 3 = 5

B B1 1 1 1 1 B

Q3 HALT HALT – Write 1

State B 0 1

Q0 Halt 1,B,R 0,1,R

Q1 2,B,L Halt 1,1,R

Q2 Halt Halt 3,B,L

Q3 - 1,Halt Halt 3,1,L

Turing MachineProgram To Subtract Unary Numbers

State, Write, Direction

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,Halt 1,B,Halt 2,B,L

Q2 3,B,R 2,0,L 2,1,L

Q3 3,B,Halt 3,B,Halt 0,B,R

Turing Machine with Halt State Program To Subtract Unary Numbers

State, Write, Direction

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,4 1,B,4 2,B,L

Q2 3,B,R 2,0,L 2,1,L

Q3 3,B,4 3,B,4 0,B,R

Q4 Halt Halt Halt

Subtracting Two Unary Numbers5 − 2 = 3

B B1 1 1 0 1 1

State Q0

1 1

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,Halt 1,B,Halt 2,B,L

Q2 3,B,R 2,0,L 2,1,L

Q3 3,B,Halt 3,B,Halt 0,B,R

Subtracting Two Unary Numbers5 − 2 = 3

B B1 1 1 0 1 1

State Q0

1 1

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,Halt 1,B,Halt 2,B,L

Q2 3,B,R 2,0,L 2,1,L

Q3 3,B,Halt 3,B,Halt 0,B,R

. . .

Subtracting Two Unary Numbers5 − 2 = 3

B B1 1 1 0 1 1

State Q1

1 1

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,Halt 1,B,Halt 2,B,L

Q2 3,B,R 2,0,L 2,1,L

Q3 3,B,Halt 3,B,Halt 0,B,R

Subtracting Two Unary Numbers5 − 2 = 3

B B1 1 1 0 1 B

State Q2

1 1

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,Halt 1,B,Halt 2,B,L

Q2 3,B,R 2,0,L 2,1,L

Q3 3,B,Halt 3,B,Halt 0,B,R

Subtracting Two Unary Numbers5 − 2 = 3

B B1 1 1 0 1 B

State Q2

1 1

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,Halt 1,B,Halt 2,B,L

Q2 3,B,R 2,0,L 2,1,L

Q3 3,B,Halt 3,B,Halt 0,B,R

Subtracting Two Unary Numbers5 − 2 = 3

B B1 1 1 0 1 B

State Q2

1 1

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,Halt 1,B,Halt 2,B,L

Q2 3,B,R 2,0,L 2,1,L

Q3 3,B,Halt 3,B,Halt 0,B,R

. . .

Subtracting Two Unary Numbers5 − 2 = 3

B B1 1 1 0 1 B

State Q3

1 1

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,Halt 1,B,Halt 2,B,L

Q2 3,B,R 2,0,L 2,1,L

Q3 3,B,Halt 3,B,Halt 0,B,R

Subtracting Two Unary Numbers5 − 2 = 3

B BB 1 1 0 1 B

State Q0

1 1

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,Halt 1,B,Halt 2,B,L

Q2 3,B,R 2,0,L 2,1,L

Q3 3,B,Halt 3,B,Halt 0,B,R

Subtracting Two Unary Numbers5 − 2 = 3

B BB 1 1 0 1 B

State Q0

1 1

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,Halt 1,B,Halt 2,B,L

Q2 3,B,R 2,0,L 2,1,L

Q3 3,B,Halt 3,B,Halt 0,B,R

. . .

Subtracting Two Unary Numbers5 − 2 = 3

B BB 1 1 0 1 B

State Q1

1 1

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,Halt 1,B,Halt 2,B,L

Q2 3,B,R 2,0,L 2,1,L

Q3 3,B,Halt 3,B,Halt 0,B,R

Subtracting Two Unary Numbers5 − 2 = 3

B BB 1 1 0 B B

State Q2

1 1

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,Halt 1,B,Halt 2,B,L

Q2 3,B,R 2,0,L 2,1,L

Q3 3,B,Halt 3,B,Halt 0,B,R

Subtracting Two Unary Numbers5 − 2 = 3

B BB 1 1 0 B B

State Q2

1 1

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,Halt 1,B,Halt 2,B,L

Q2 3,B,R 2,0,L 2,1,L

Q3 3,B,Halt 3,B,Halt 0,B,R

. . .

Subtracting Two Unary Numbers5 − 2 = 3

B BB 1 1 0 B B

State Q3

1 1

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,Halt 1,B,Halt 2,B,L

Q2 3,B,R 2,0,L 2,1,L

Q3 3,B,Halt 3,B,Halt 0,B,R

Subtracting Two Unary Numbers5 − 2 = 3

B BB B 1 0 B B

State Q0

1 1

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,Halt 1,B,Halt 2,B,L

Q2 3,B,R 2,0,L 2,1,L

Q3 3,B,Halt 3,B,Halt 0,B,R

Subtracting Two Unary Numbers5 − 2 = 3

B BB B 1 0 B B

State Q0

1 1

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,Halt 1,B,Halt 2,B,L

Q2 3,B,R 2,0,L 2,1,L

Q3 3,B,Halt 3,B,Halt 0,B,R

. . .

Subtracting Two Unary Numbers5 − 2 = 3

B BB B 1 0 B B

Q1

1 1

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,Halt 1,B,Halt 2,B,L

Q2 3,B,R 2,0,L 1,1,L

Q3 3,B,Halt 3,B,Halt 0,B,R

Subtracting Two Unary Numbers5 − 2 = 3

B BB B 1 B B B

Q1 Halt Write Blank

1 1

State B 0 1

Q0 1,B,L 0,0,R 0,1,R

Q1 1,B,Halt 1,B,Halt 2,B,L

Q2 3,B,R 2,0,L 1,1,L

Q3 3,B,Halt 3,B,Halt 0,B,R