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Variations of the Turing Machine

Variations of the Turing Machine. The Standard Model. Infinite Tape. Read-Write Head. (Left or Right). Control Unit. Deterministic. Variations of the Standard Model. Turing Machines with Stay-Option Turing Machines with Semi-Infinite Tape The Off-Line Turing Machine

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Variations of the Turing Machine

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  1. Variationsof theTuring Machine

  2. The Standard Model Infinite Tape Read-Write Head (Left or Right) Control Unit Deterministic

  3. Variations of the Standard Model • Turing Machines with Stay-Option • Turing Machines with Semi-Infinite Tape • The Off-Line Turing Machine • Multitape Turing Machines • Multidimensional Turing Machines • Nondeterministic Turing Machines

  4. The variations form different Turing Machine Classes We want to prove: Each Class has the same power with the Standard Model

  5. Same Power of two classes means: Take machine of first class There is a machine of second class such that: (second class is at least as powerful as first class) And vice-versa

  6. A technique to prove same power: Simulation Simulate the machine of one class with a machine of the other class Second Class Simulation Machine First Class Original Machine

  7. Configurations in the Original Machine correspond to configurations in the Simulation Machine Original Machine: Simulation Machine:

  8. Final Configuration Original Machine: Simulation Machine: The Simulation Machine and the Original Machine will accept the same language

  9. Turing Machines with Stay-Option The head can stay in the same position Left, Right, Stay L,R,S: moves

  10. Example: Time 1 Time 2

  11. Theorem: Machines with Stay-Option have the same power with the standard Turing machines

  12. Proof: Part1 -- Stay-Option Machines are at least as powerful as standard machines Trivial proof: A standard machine is also a Stay-Option machine (that never uses the S move)

  13. Part2 -- Standard Machines are at least as powerful as Stay-Option machines Proof: a standard machine can simulate a Stay-Option machine

  14. Stay-Option Machine Simulation in Standard Machine Similar for Right moves

  15. Stay-Option Machine Simulation in Standard Machine For every symbol

  16. Example Stay-Option Machine: 1 2 Simulation in Standard Machine: 1 2 3

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