Download - Variants of Turing Machine
![Page 1: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/1.jpg)
Costas Busch - RPI 1
Variationsof the
Turing Machine
![Page 2: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/2.jpg)
Costas Busch - RPI 2
Variations of the Standard Model
• Stay-Option • Semi-Infinite Tape• Off-Line• Multitape• Multidimensional• Nondeterministic
Turing machines with:
![Page 3: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/3.jpg)
Costas Busch - RPI 3
Same Power of two classes means:
For any machine of first class 1M
there is a machine of second class 2M
such that: )()( 21 MLML
And vice-versa
![Page 4: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/4.jpg)
Costas Busch - RPI 4
Turing Machines with Stay-Option
The head can stay in the same position
a a c b a cb b a a
Left, Right, Stay
L,R,S: moves
![Page 5: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/5.jpg)
Costas Busch - RPI 5
Example:
a a c b a cb b a a
Time 1
b a c b a cb b a a
Time 2
1q 2q
1q
2q
Sba ,
![Page 6: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/6.jpg)
Costas Busch - RPI 6
1q 2qSba ,
1q 2qLba ,
3qRxx ,
Stay-Option Machine
Simulation in Standard Machine
For every symbol x
![Page 7: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/7.jpg)
Costas Busch - RPI 7
Example
a a b a
1q
Stay-Option Machine:
1
b a b a
2q
2
1q 2qSba ,
Simulation in Standard Machine:
a a b a
1q
1
b a b a
2q
2
b a b a
3q
3
![Page 8: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/8.jpg)
Costas Busch - RPI 8
Standard Machine--Multiple Track Tape
bd
abbaac
track 1
track 2
one symbol
![Page 9: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/9.jpg)
Costas Busch - RPI 9
Semi-Infinite Tape
.........# a b a c
![Page 10: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/10.jpg)
Costas Busch - RPI 10
The Off-Line Machine
Control Unit
Input File
Tape
read-only
a b c
d eg
read-write
![Page 11: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/11.jpg)
Costas Busch - RPI 11
1. Copy input file to tape
Input File
a b c
Tape
a b c
Standard machine
Off-line machine
a b c
![Page 12: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/12.jpg)
Costas Busch - RPI 12
2. Do computations as in Turing machine
Input File
a b c
Tape
a b c
a b c
1q
1q
Standard machine
Off-line machine
![Page 13: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/13.jpg)
Costas Busch - RPI 13
Standard Turing machines simulate Off-line machines:
Use a Standard machine with four track tapeto keep track ofthe Off-line input file and tape contents
![Page 14: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/14.jpg)
Costas Busch - RPI 14
Multitape Turing Machines
a b c e f g
Control unit
Tape 1 Tape 2
Input
![Page 15: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/15.jpg)
Costas Busch - RPI 15
a b c e f g
1q 1q
a g c e d g
2q 2q
Time 1
Time 2
RLdgfb ,),,(),( 1q 2q
Tape 1 Tape 2
![Page 16: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/16.jpg)
Costas Busch - RPI 16
Same power doesn’t imply same speed:
Language }{ nnbaL
Acceptance Time
Standard machine
Two-tape machine
2n
n
![Page 17: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/17.jpg)
Costas Busch - RPI 17
NonDeterministic Turing Machines
Lba ,
Rca ,
1q
2q
3q
Non Deterministic Choice
![Page 18: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/18.jpg)
Costas Busch - RPI 18
a b c
1q
Lba ,
Rca ,
1q
2q
3q
Time 0
Time 1
b b c
2q
c b c
3q
Choice 1 Choice 2
![Page 19: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/19.jpg)
Costas Busch - RPI 19
Input string is accepted if this a possible computationw
yqxwq f0
Initial configuration Final Configuration
Final state
![Page 20: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/20.jpg)
Costas Busch - RPI 20
Non-Deterministic Choices
Computation 1
1q
2q
4q
3q
5q
6q 7q
![Page 21: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/21.jpg)
Costas Busch - RPI 21
Non-Deterministic Choices
Computation 2
1q
2q
4q
3q
5q
6q 7q
![Page 22: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/22.jpg)
Costas Busch - RPI 22
Theorem: NonDeterministic Machines have the same power with Deterministic machines
![Page 23: Variants of Turing Machine](https://reader036.vdocuments.us/reader036/viewer/2022062503/5881686f1a28ab80508b758f/html5/thumbnails/23.jpg)
Costas Busch - RPI 23
Remark: The simulation in the Deterministic machine takes time exponential time compared to the NonDeterministic machine