# 6/3/2014 A Universal Machine A universal Turing machine is designed to simulate the computations of an arbitrary Turing machine M. R(M)w Universal machine.

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6/3/2014 A Universal Machine A universal Turing machine is designed to simulate the computations of an arbitrary Turing machine M. R(M)w Universal machine U M halts with w M does not halt with input w Accept Loop R(M) represents a Turing machine M that accepts by halting. W represents the input string.

6/3/2014 A Universal Machine R(M)w Universal machine U M halts with w M does not halt with input w Accept Loop If M halts and accepts input w ===> U halts and accepts input W too If M does not halt with W ===>Neither does U.

6/3/2014 Turing Machine Example with Halts q0q0 q1q1 q2q2 1/1 L 0/0 L 1/1 RB/B R Run JFLAP

6/3/2014 Transition Function 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) en(q i )0en(x)0en(q j )0en(y)0en(d)

6/3/2014 Symbol -- Encoding 01 111 B111 q0q0 1 q1q1 11 … qnqn 1 n+1 L1 R11 Input alphabet {0,1} tape alphabet {0, 1, B} states q0, q1 ….

6/3/2014 Universal Machine Example q0q0 q1q1 q2q2 1/1 L 0/0 L 1/1 RB/B R 00010111011011101100110101010100….00….000

6/3/2014 Three-tape Deterministic Universal Machine 00010111011011101... 00010111011011101100110101010100….00….000 tape 1:

6/3/2014 Three-tape Deterministic Universal Machine 00010111011011101... 00010111011011101100110101010100….00….000 tape 1: tape 2: 1B current / updated state Put q 0 as the start state

6/3/2014 Three-tape Deterministic Universal Machine 00010111011011101... 00010111011011101100110101010100….00….000 tape 1: tape 3: tape 2: 1B current / updated state B1011B string w

6/3/2014 Three-tape Deterministic Universal Machine 00010111011011101... 00010111011011101100110101010100….00….000 tape 1: tape 3: tape 2: 1B current / updated state B1011B string w

6/3/2014 Three-tape Deterministic Universal Machine 00010111011011101100 00010111011011101100110101010100….00….000 tape 1: tape 3: tape 2: 11B current / updated state B1011B string w

6/3/2014 Three-tape Deterministic Universal Machine...110110111011011.. 00010111011011101100110101010100….00….000 tape 1: tape 3: tape 2: 11B current / updated state B1011B string w

6/3/2014 Three-tape Deterministic Universal Machine...110110111011011.. 00010111011011101100110101010100….00….000 tape 1: tape 3: tape 2: 111B current / updated state B1011B string w

6/3/2014 Three-tape Deterministic Universal Machine...110110111011011.. 00010111011011101100110101010100….00….000 tape 1: tape 3: tape 2: 111B current / updated state B1011B string w U halts accepting the input if there is no such transition!!

6/3/2014 CSE355 An Introduction to the Theory of Computer Science Good luck your finals Enjoy your Winter break … &

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