A Universal Machine A universal Turing machine is

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

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

Turing Machine Example with Halts 0/0 L q 0 B/B R q 1 1/1 R q 2 1/1 L Run JFLAP

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

Symbol -- Encoding Input alphabet {0, 1} 0 1 1 11 tape alphabet {0, 1, B} B 111 q 0 1 q 1 11 states q 0, q 1 …. … qn 1 n+1 L 1 R 11

Universal Machine Example 0/0 L q 0 B/B R q 1 1/1 R q 2 1/1 L 000101110110011010100…. 000

Three-tape Deterministic Universal Machine 000101110110011010100…. 000 tape 1: 0001011101. . .

Three-tape Deterministic Universal Machine 000101110110011010100…. 000 tape 1: 0001011101. . . tape 2: 1 B Put q 0 as the start state current / updated state

Three-tape Deterministic Universal Machine 000101110110011010100…. 000 tape 1: 0001011101. . . tape 2: 1 tape 3: current / updated state B B 1 0 1 1 B string w

Three-tape Deterministic Universal Machine 000101110110011010100…. 000 tape 1: 0001011101. . . tape 2: 1 tape 3: current / updated state B B 1 0 1 1 B string w

Three-tape Deterministic Universal Machine 000101110110011010100…. 000 tape 1: 0 0 0 1 1 1 0 0 tape 2: 1 tape 3: 1 B B 1 0 current / updated state 1 1 B string w

Three-tape Deterministic Universal Machine 000101110110011010100…. 000 tape 1: . . . 11011011. . tape 2: 1 1 B tape 3: B 1 0 current / updated state 1 1 B string w

Three-tape Deterministic Universal Machine 000101110110011010100…. 000 tape 1: . . . 11011011. . tape 2: 1 1 1 B tape 3: B 1 0 1 current / updated state 1 B string w

Three-tape Deterministic Universal Machine 000101110110011010100…. 000 tape 1: . . . 11011011. . tape 2: 1 1 1 B tape 3: B 1 0 1 current / updated state 1 B string w U halts accepting the input if there is no such transition!!

CSE 355 An Introduction to the Theory of Computer Science Good luck your finals & Enjoy your Winter break …