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A Universal Machine

A Universal Machine. A universal Turing machine is designed to simulate the computations of an arbitrary Turing machine M. Universal machine U. M halts with w. Accept. R(M) w. Loop. M does not halt with input w.

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A Universal Machine

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  1. A Universal Machine A universal Turing machine is designed to simulate the computations of an arbitrary Turing machine M. Universal machine U M halts with w Accept R(M)w Loop M does not halt with input w R(M) represents a Turing machine M that accepts by halting.W represents the input string.

  2. A Universal Machine Universal machine U M halts with w Accept R(M)w Loop M does not halt with input w If M halts and accepts input w ===>U halts and accepts input W tooIf M does not halt with W ===> Neither does U.

  3. q0 q1 q2 Turing Machine Example with Halts 0/0 L B/B R 1/1 R 1/1 L Run JFLAP

  4. Transition Function en(qi)0en(x)0en(qj)0en(y)0en(d) Input alphabet {0,1}, x and y belongs to {0,1,B}tape alphabet {0, 1, B}states q0, q1 ….move to left (L) or right (R)

  5. Symbol -- Encoding Input alphabet {0,1}tape alphabet {0, 1, B}states q0, q1 ….

  6. 0/0 L B/B R 1/1 R q0 q1 q2 1/1 L Universal Machine Example 00010111011011101100110101010100….00….000

  7. Three-tape Deterministic Universal Machine 00010111011011101100110101010100….00….000 tape 1:

  8. Three-tape Deterministic Universal Machine 00010111011011101100110101010100….00….000 tape 1: current / updated state tape 2: Put q0 as the start state

  9. Three-tape Deterministic Universal Machine 00010111011011101100110101010100….00….000 tape 1: current / updated state tape 2: string w tape 3:

  10. Three-tape Deterministic Universal Machine 00010111011011101100110101010100….00….000 tape 1: current / updated state tape 2: string w tape 3:

  11. Three-tape Deterministic Universal Machine 00010111011011101100110101010100….00….000 tape 1: current / updated state tape 2: string w tape 3:

  12. Three-tape Deterministic Universal Machine 00010111011011101100110101010100….00….000 tape 1: current / updated state tape 2: string w tape 3:

  13. Three-tape Deterministic Universal Machine 00010111011011101100110101010100….00….000 tape 1: current / updated state tape 2: string w tape 3:

  14. Three-tape Deterministic Universal Machine 00010111011011101100110101010100….00….000 tape 1: current / updated state tape 2: string w tape 3: U halts accepting the input if there is no such transition!!

  15. CSE355An Introduction to the Theory of Computer Science Good luck your finals & Enjoy your Winter break …

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