Variations of the Turing Machine part 2 1
![Variations of the Turing Machine part 2 1 Variations of the Turing Machine part 2 1](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-1.jpg)
![Standard Machine--Multiple Track Tape track 1 track 2 one symbol 2 Standard Machine--Multiple Track Tape track 1 track 2 one symbol 2](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-2.jpg)
![track 1 track 2 3 track 1 track 2 3](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-3.jpg)
![Semi-Infinite Tape. . 4 Semi-Infinite Tape. . 4](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-4.jpg)
![Standard Turing machines simulate Semi-infinite tape machines Trivial 5 Standard Turing machines simulate Semi-infinite tape machines Trivial 5](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-5.jpg)
![Semi-infinite tape machines simulate Standard Turing machines Turing machine. . . . Semi-infinite tape Semi-infinite tape machines simulate Standard Turing machines Turing machine. . . . Semi-infinite tape](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-6.jpg)
![Turing machine. . . . reference point Semi-infinite tape with two tracks Right part Turing machine. . . . reference point Semi-infinite tape with two tracks Right part](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-7.jpg)
![Turing machine Semi-infinite tape machine Left part Right part 8 Turing machine Semi-infinite tape machine Left part Right part 8](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-8.jpg)
![Turing machine Semi-infinite tape machine Right part Left part For all symbols x 9 Turing machine Semi-infinite tape machine Right part Left part For all symbols x 9](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-9.jpg)
![Time 1 Turing machine . . . . Semi-infinite tape Right part Left part Time 1 Turing machine . . . . Semi-infinite tape Right part Left part](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-10.jpg)
![Time 2 Turing machine . . . . Semi-infinite tape Right part Left part Time 2 Turing machine . . . . Semi-infinite tape Right part Left part](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-11.jpg)
![At the border: Semi-infinite tape machine Right part Left part 12 At the border: Semi-infinite tape machine Right part Left part 12](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-12.jpg)
![Semi-infinite tape Right part Time 1 Left part Right part Left part . . Semi-infinite tape Right part Time 1 Left part Right part Left part . .](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-13.jpg)
![Theorem: Semi-infinite tape machines have the same power with Standard Turing machines 14 Theorem: Semi-infinite tape machines have the same power with Standard Turing machines 14](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-14.jpg)
![The Off-Line Machine Input File read-only Control Unit Tape read-write 15 The Off-Line Machine Input File read-only Control Unit Tape read-write 15](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-15.jpg)
![Off-line Machines simulate Turing Machines Off-line machine: 1. Copy input file to tape 2. Off-line Machines simulate Turing Machines Off-line machine: 1. Copy input file to tape 2.](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-16.jpg)
![Turing Machine Off-line Machine Input File Tape 1. Copy input file to tape 17 Turing Machine Off-line Machine Input File Tape 1. Copy input file to tape 17](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-17.jpg)
![Turing Machine Off-line Machine Input File Tape 2. Do computations as in Turing machine Turing Machine Off-line Machine Input File Tape 2. Do computations as in Turing machine](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-18.jpg)
![Turing Machines simulate Off-line machines Use a Standard machine with four track tape to Turing Machines simulate Off-line machines Use a Standard machine with four track tape to](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-19.jpg)
![Off-line Machine Input File Tape Four track tape -- Standard Machine input file head Off-line Machine Input File Tape Four track tape -- Standard Machine input file head](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-20.jpg)
![Reference point input file head position tape head position Repeat for each state transition: Reference point input file head position tape head position Repeat for each state transition:](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-21.jpg)
![Theorem: Off-line machines have the same power with Stansard machines 22 Theorem: Off-line machines have the same power with Stansard machines 22](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-22.jpg)
![Multitape Turing Machines Control unit Input tape 1 tape 2 23 Multitape Turing Machines Control unit Input tape 1 tape 2 23](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-23.jpg)
![Time 1 Time 2 24 Time 1 Time 2 24](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-24.jpg)
![Multitape machines simulate Standard Machines Just use one tape 25 Multitape machines simulate Standard Machines Just use one tape 25](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-25.jpg)
![Standard machines simulate Multitape machines Standard machine: Use a multi-track tape A tape of Standard machines simulate Multitape machines Standard machine: Use a multi-track tape A tape of](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-26.jpg)
![Multitape Machine Tape 1 Tape 2 Four track tape -- Standard Machine Tape 1 Multitape Machine Tape 1 Tape 2 Four track tape -- Standard Machine Tape 1](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-27.jpg)
![Reference point Tape 1 head position Tape 2 head position Repeat for each state Reference point Tape 1 head position Tape 2 head position Repeat for each state](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-28.jpg)
![Theorem: Multi-tape machines have the same power with Standard Turing Machines 29 Theorem: Multi-tape machines have the same power with Standard Turing Machines 29](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-29.jpg)
![Same power doesn’t mean same speed: Language Acceptance Time Standard machine Two-tape machine 30 Same power doesn’t mean same speed: Language Acceptance Time Standard machine Two-tape machine 30](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-30.jpg)
![Standard machine: Go back and forth times Two-tape machine: Copy Leave to tape 2 Standard machine: Go back and forth times Two-tape machine: Copy Leave to tape 2](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-31.jpg)
![Multi. Dimensional Turing Machines Two-dimensional tape MOVES: L, R, U, D U: up D: Multi. Dimensional Turing Machines Two-dimensional tape MOVES: L, R, U, D U: up D:](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-32.jpg)
![Multidimensional machines simulate Standard machines Just use one dimension 33 Multidimensional machines simulate Standard machines Just use one dimension 33](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-33.jpg)
![Standard machines simulate Multidimensional machines Standard machine: Use a two track tape Store symbols Standard machines simulate Multidimensional machines Standard machine: Use a two track tape Store symbols](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-34.jpg)
![Two-dimensional machine Standard Machine symbols coordinates 35 Two-dimensional machine Standard Machine symbols coordinates 35](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-35.jpg)
![Simulation: Repeat for each transition Update current symbol Compute coordinates of next position Go Simulation: Repeat for each transition Update current symbol Compute coordinates of next position Go](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-36.jpg)
![Theorem: Multi. Dimensional Machines have the same power with Turing Machines 37 Theorem: Multi. Dimensional Machines have the same power with Turing Machines 37](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-37.jpg)
![Non. Deterministic Turing Machines Non Deterministic Choice 38 Non. Deterministic Turing Machines Non Deterministic Choice 38](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-38.jpg)
![TIME 0 Choice 1 TIME 1 Choice 2 39 TIME 0 Choice 1 TIME 1 Choice 2 39](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-39.jpg)
![Input is accepted if this a possible computation Initial configuration Final Configuration Final state Input is accepted if this a possible computation Initial configuration Final Configuration Final state](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-40.jpg)
![Non. Deterministic Machines simulate Standard (deterministic) Machines Every deterministic machine is also a nondeterministic Non. Deterministic Machines simulate Standard (deterministic) Machines Every deterministic machine is also a nondeterministic](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-41.jpg)
![Deterministic machines simulate Non. Deterministic machines Deterministic machine: Keeps track of all possible computations Deterministic machines simulate Non. Deterministic machines Deterministic machine: Keeps track of all possible computations](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-42.jpg)
![Non-Deterministic Choices Computation 1 43 Non-Deterministic Choices Computation 1 43](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-43.jpg)
![Non-Deterministic Choices Computation 2 44 Non-Deterministic Choices Computation 2 44](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-44.jpg)
![Simulation Deterministic machine: Keeps track of all possible computations Stores computations in a two-dimensional Simulation Deterministic machine: Keeps track of all possible computations Stores computations in a two-dimensional](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-45.jpg)
![TIME 0 Non. Deterministic Computation 1 46 TIME 0 Non. Deterministic Computation 1 46](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-46.jpg)
![TIME 1 Non. Deterministic Choice 1 Choice 2 Deterministic Computation 1 Computation 2 47 TIME 1 Non. Deterministic Choice 1 Choice 2 Deterministic Computation 1 Computation 2 47](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-47.jpg)
![Repeat Execute a step in each computation: If there is a choice in current Repeat Execute a step in each computation: If there is a choice in current](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-48.jpg)
![Theorem: Non. Deterministic Machines have the same power with deterministic machines 49 Theorem: Non. Deterministic Machines have the same power with deterministic machines 49](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-49.jpg)
![Remark: The simulation in the deterministic Machine takes time exponential time compared to Non. Remark: The simulation in the deterministic Machine takes time exponential time compared to Non.](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-50.jpg)
![Polynomial Time in Non. Deterministic Machine NP-Time Polynomial Time in Deterministic Machine P-Time Fundamental Polynomial Time in Non. Deterministic Machine NP-Time Polynomial Time in Deterministic Machine P-Time Fundamental](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-51.jpg)
- Slides: 51
![Variations of the Turing Machine part 2 1 Variations of the Turing Machine part 2 1](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-1.jpg)
Variations of the Turing Machine part 2 1
![Standard MachineMultiple Track Tape track 1 track 2 one symbol 2 Standard Machine--Multiple Track Tape track 1 track 2 one symbol 2](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-2.jpg)
Standard Machine--Multiple Track Tape track 1 track 2 one symbol 2
![track 1 track 2 3 track 1 track 2 3](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-3.jpg)
track 1 track 2 3
![SemiInfinite Tape 4 Semi-Infinite Tape. . 4](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-4.jpg)
Semi-Infinite Tape. . 4
![Standard Turing machines simulate Semiinfinite tape machines Trivial 5 Standard Turing machines simulate Semi-infinite tape machines Trivial 5](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-5.jpg)
Standard Turing machines simulate Semi-infinite tape machines Trivial 5
![Semiinfinite tape machines simulate Standard Turing machines Turing machine Semiinfinite tape Semi-infinite tape machines simulate Standard Turing machines Turing machine. . . . Semi-infinite tape](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-6.jpg)
Semi-infinite tape machines simulate Standard Turing machines Turing machine. . . . Semi-infinite tape machine. . 6
![Turing machine reference point Semiinfinite tape with two tracks Right part Turing machine. . . . reference point Semi-infinite tape with two tracks Right part](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-7.jpg)
Turing machine. . . . reference point Semi-infinite tape with two tracks Right part Left part . . 7
![Turing machine Semiinfinite tape machine Left part Right part 8 Turing machine Semi-infinite tape machine Left part Right part 8](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-8.jpg)
Turing machine Semi-infinite tape machine Left part Right part 8
![Turing machine Semiinfinite tape machine Right part Left part For all symbols x 9 Turing machine Semi-infinite tape machine Right part Left part For all symbols x 9](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-9.jpg)
Turing machine Semi-infinite tape machine Right part Left part For all symbols x 9
![Time 1 Turing machine Semiinfinite tape Right part Left part Time 1 Turing machine . . . . Semi-infinite tape Right part Left part](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-10.jpg)
Time 1 Turing machine . . . . Semi-infinite tape Right part Left part . . 10
![Time 2 Turing machine Semiinfinite tape Right part Left part Time 2 Turing machine . . . . Semi-infinite tape Right part Left part](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-11.jpg)
Time 2 Turing machine . . . . Semi-infinite tape Right part Left part . . 11
![At the border Semiinfinite tape machine Right part Left part 12 At the border: Semi-infinite tape machine Right part Left part 12](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-12.jpg)
At the border: Semi-infinite tape machine Right part Left part 12
![Semiinfinite tape Right part Time 1 Left part Right part Left part Semi-infinite tape Right part Time 1 Left part Right part Left part . .](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-13.jpg)
Semi-infinite tape Right part Time 1 Left part Right part Left part . . Time 2. . 13
![Theorem Semiinfinite tape machines have the same power with Standard Turing machines 14 Theorem: Semi-infinite tape machines have the same power with Standard Turing machines 14](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-14.jpg)
Theorem: Semi-infinite tape machines have the same power with Standard Turing machines 14
![The OffLine Machine Input File readonly Control Unit Tape readwrite 15 The Off-Line Machine Input File read-only Control Unit Tape read-write 15](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-15.jpg)
The Off-Line Machine Input File read-only Control Unit Tape read-write 15
![Offline Machines simulate Turing Machines Offline machine 1 Copy input file to tape 2 Off-line Machines simulate Turing Machines Off-line machine: 1. Copy input file to tape 2.](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-16.jpg)
Off-line Machines simulate Turing Machines Off-line machine: 1. Copy input file to tape 2. Continue computation as in Standard Turing machine 16
![Turing Machine Offline Machine Input File Tape 1 Copy input file to tape 17 Turing Machine Off-line Machine Input File Tape 1. Copy input file to tape 17](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-17.jpg)
Turing Machine Off-line Machine Input File Tape 1. Copy input file to tape 17
![Turing Machine Offline Machine Input File Tape 2 Do computations as in Turing machine Turing Machine Off-line Machine Input File Tape 2. Do computations as in Turing machine](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-18.jpg)
Turing Machine Off-line Machine Input File Tape 2. Do computations as in Turing machine 18
![Turing Machines simulate Offline machines Use a Standard machine with four track tape to Turing Machines simulate Off-line machines Use a Standard machine with four track tape to](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-19.jpg)
Turing Machines simulate Off-line machines Use a Standard machine with four track tape to keep track of the Off-line input file and tape contents 19
![Offline Machine Input File Tape Four track tape Standard Machine input file head Off-line Machine Input File Tape Four track tape -- Standard Machine input file head](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-20.jpg)
Off-line Machine Input File Tape Four track tape -- Standard Machine input file head position tape head position 20
![Reference point input file head position tape head position Repeat for each state transition Reference point input file head position tape head position Repeat for each state transition:](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-21.jpg)
Reference point input file head position tape head position Repeat for each state transition: Return to reference point Find current input file symbol Find current tape symbol make transition 21
![Theorem Offline machines have the same power with Stansard machines 22 Theorem: Off-line machines have the same power with Stansard machines 22](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-22.jpg)
Theorem: Off-line machines have the same power with Stansard machines 22
![Multitape Turing Machines Control unit Input tape 1 tape 2 23 Multitape Turing Machines Control unit Input tape 1 tape 2 23](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-23.jpg)
Multitape Turing Machines Control unit Input tape 1 tape 2 23
![Time 1 Time 2 24 Time 1 Time 2 24](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-24.jpg)
Time 1 Time 2 24
![Multitape machines simulate Standard Machines Just use one tape 25 Multitape machines simulate Standard Machines Just use one tape 25](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-25.jpg)
Multitape machines simulate Standard Machines Just use one tape 25
![Standard machines simulate Multitape machines Standard machine Use a multitrack tape A tape of Standard machines simulate Multitape machines Standard machine: Use a multi-track tape A tape of](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-26.jpg)
Standard machines simulate Multitape machines Standard machine: Use a multi-track tape A tape of the Multiple tape machine corresponds to a pair of tracks 26
![Multitape Machine Tape 1 Tape 2 Four track tape Standard Machine Tape 1 Multitape Machine Tape 1 Tape 2 Four track tape -- Standard Machine Tape 1](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-27.jpg)
Multitape Machine Tape 1 Tape 2 Four track tape -- Standard Machine Tape 1 head position Tape 2 head position 27
![Reference point Tape 1 head position Tape 2 head position Repeat for each state Reference point Tape 1 head position Tape 2 head position Repeat for each state](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-28.jpg)
Reference point Tape 1 head position Tape 2 head position Repeat for each state transition: Return to reference point Find current symbol on Tape 1 Find current symbol on Tape 2 make transition 28
![Theorem Multitape machines have the same power with Standard Turing Machines 29 Theorem: Multi-tape machines have the same power with Standard Turing Machines 29](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-29.jpg)
Theorem: Multi-tape machines have the same power with Standard Turing Machines 29
![Same power doesnt mean same speed Language Acceptance Time Standard machine Twotape machine 30 Same power doesn’t mean same speed: Language Acceptance Time Standard machine Two-tape machine 30](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-30.jpg)
Same power doesn’t mean same speed: Language Acceptance Time Standard machine Two-tape machine 30
![Standard machine Go back and forth times Twotape machine Copy Leave to tape 2 Standard machine: Go back and forth times Two-tape machine: Copy Leave to tape 2](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-31.jpg)
Standard machine: Go back and forth times Two-tape machine: Copy Leave to tape 2 ( steps) to tape 1 ( steps) Compare tape 1 and tape 2 31
![Multi Dimensional Turing Machines Twodimensional tape MOVES L R U D U up D Multi. Dimensional Turing Machines Two-dimensional tape MOVES: L, R, U, D U: up D:](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-32.jpg)
Multi. Dimensional Turing Machines Two-dimensional tape MOVES: L, R, U, D U: up D: down HEAD Position: +2, -1 32
![Multidimensional machines simulate Standard machines Just use one dimension 33 Multidimensional machines simulate Standard machines Just use one dimension 33](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-33.jpg)
Multidimensional machines simulate Standard machines Just use one dimension 33
![Standard machines simulate Multidimensional machines Standard machine Use a two track tape Store symbols Standard machines simulate Multidimensional machines Standard machine: Use a two track tape Store symbols](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-34.jpg)
Standard machines simulate Multidimensional machines Standard machine: Use a two track tape Store symbols in track 1 Store coordinates in track 2 34
![Twodimensional machine Standard Machine symbols coordinates 35 Two-dimensional machine Standard Machine symbols coordinates 35](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-35.jpg)
Two-dimensional machine Standard Machine symbols coordinates 35
![Simulation Repeat for each transition Update current symbol Compute coordinates of next position Go Simulation: Repeat for each transition Update current symbol Compute coordinates of next position Go](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-36.jpg)
Simulation: Repeat for each transition Update current symbol Compute coordinates of next position Go to new position 36
![Theorem Multi Dimensional Machines have the same power with Turing Machines 37 Theorem: Multi. Dimensional Machines have the same power with Turing Machines 37](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-37.jpg)
Theorem: Multi. Dimensional Machines have the same power with Turing Machines 37
![Non Deterministic Turing Machines Non Deterministic Choice 38 Non. Deterministic Turing Machines Non Deterministic Choice 38](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-38.jpg)
Non. Deterministic Turing Machines Non Deterministic Choice 38
![TIME 0 Choice 1 TIME 1 Choice 2 39 TIME 0 Choice 1 TIME 1 Choice 2 39](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-39.jpg)
TIME 0 Choice 1 TIME 1 Choice 2 39
![Input is accepted if this a possible computation Initial configuration Final Configuration Final state Input is accepted if this a possible computation Initial configuration Final Configuration Final state](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-40.jpg)
Input is accepted if this a possible computation Initial configuration Final Configuration Final state 40
![Non Deterministic Machines simulate Standard deterministic Machines Every deterministic machine is also a nondeterministic Non. Deterministic Machines simulate Standard (deterministic) Machines Every deterministic machine is also a nondeterministic](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-41.jpg)
Non. Deterministic Machines simulate Standard (deterministic) Machines Every deterministic machine is also a nondeterministic machine 41
![Deterministic machines simulate Non Deterministic machines Deterministic machine Keeps track of all possible computations Deterministic machines simulate Non. Deterministic machines Deterministic machine: Keeps track of all possible computations](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-42.jpg)
Deterministic machines simulate Non. Deterministic machines Deterministic machine: Keeps track of all possible computations 42
![NonDeterministic Choices Computation 1 43 Non-Deterministic Choices Computation 1 43](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-43.jpg)
Non-Deterministic Choices Computation 1 43
![NonDeterministic Choices Computation 2 44 Non-Deterministic Choices Computation 2 44](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-44.jpg)
Non-Deterministic Choices Computation 2 44
![Simulation Deterministic machine Keeps track of all possible computations Stores computations in a twodimensional Simulation Deterministic machine: Keeps track of all possible computations Stores computations in a two-dimensional](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-45.jpg)
Simulation Deterministic machine: Keeps track of all possible computations Stores computations in a two-dimensional tape 45
![TIME 0 Non Deterministic Computation 1 46 TIME 0 Non. Deterministic Computation 1 46](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-46.jpg)
TIME 0 Non. Deterministic Computation 1 46
![TIME 1 Non Deterministic Choice 1 Choice 2 Deterministic Computation 1 Computation 2 47 TIME 1 Non. Deterministic Choice 1 Choice 2 Deterministic Computation 1 Computation 2 47](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-47.jpg)
TIME 1 Non. Deterministic Choice 1 Choice 2 Deterministic Computation 1 Computation 2 47
![Repeat Execute a step in each computation If there is a choice in current Repeat Execute a step in each computation: If there is a choice in current](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-48.jpg)
Repeat Execute a step in each computation: If there is a choice in current computation: replicate configuration change the state in the replica 48
![Theorem Non Deterministic Machines have the same power with deterministic machines 49 Theorem: Non. Deterministic Machines have the same power with deterministic machines 49](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-49.jpg)
Theorem: Non. Deterministic Machines have the same power with deterministic machines 49
![Remark The simulation in the deterministic Machine takes time exponential time compared to Non Remark: The simulation in the deterministic Machine takes time exponential time compared to Non.](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-50.jpg)
Remark: The simulation in the deterministic Machine takes time exponential time compared to Non. Deterministic machines 50
![Polynomial Time in Non Deterministic Machine NPTime Polynomial Time in Deterministic Machine PTime Fundamental Polynomial Time in Non. Deterministic Machine NP-Time Polynomial Time in Deterministic Machine P-Time Fundamental](https://slidetodoc.com/presentation_image/502664018d4910ef8d47c22437b6e291/image-51.jpg)
Polynomial Time in Non. Deterministic Machine NP-Time Polynomial Time in Deterministic Machine P-Time Fundamental Problem: P = NP ? 51
Alan mathison turing
Turing macine
Halting problem of turing machine
Turing machine examples
More powerful than turing machine
Instantaneous description of turing machine
Turing machine for wcw
Turing machine formal definition
Turing machine examples
Turing machine simulator tutorial
The ghost in the quantum turing machine
Multistack turing machine
Bas luttik
Turing machine
Formal definition of turing machine
Multidimensional turing machine
Mechanical turing machine
Nondeterministic turing machine
Wcw turing machine
Turing machine
Atm turing machine
Turing macine
Turing machine
Turing machine
Turing machine
Turing machine is more powerful than:
Extensions of turing machine
A deterministic turing machine is: *
Turing machine
Turing machine
Turing machine
Power point turing complete
Turing machine algorithm
Turing machine is more powerful than: *
Busy beaver turing machine
How to prove if a language is decidable
Machine countable or uncountable
Valuation of variations
Types of variation
Graph of inverse variation
Kwhl chart
Cultural variations in attachment
Computer organization & architecture: themes and variations
Thermal stability of bjt
Super bowl squares variations
Varies jointly example
Variations pathologiques de la température
Uni-factor theory of intelligence by alfred binet
Sin rule for sides
Variations de stock
Social variation
Possible variations