A universal machine
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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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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

R(M) represents a Turing machine M that accepts by halting.W represents the input string.


A universal machine1

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.


Turing machine example with halts

q0

q1

q2

Turing Machine Example with Halts

0/0 L

B/B R

1/1 R

1/1 L

Run JFLAP


Transition function

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)


Symbol encoding

Symbol -- Encoding

Input alphabet {0,1}tape alphabet {0, 1, B}states q0, q1 ….


Universal machine example

0/0 L

B/B R

1/1 R

q0

q1

q2

1/1 L

Universal Machine Example

00010111011011101100110101010100….00….000


Three tape deterministic universal machine

Three-tape Deterministic Universal Machine

00010111011011101100110101010100….00….000

tape 1:


Three tape deterministic universal machine1

Three-tape Deterministic Universal Machine

00010111011011101100110101010100….00….000

tape 1:

current / updated state

tape 2:

Put q0 as the start state


Three tape deterministic universal machine2

Three-tape Deterministic Universal Machine

00010111011011101100110101010100….00….000

tape 1:

current / updated state

tape 2:

string w

tape 3:


Three tape deterministic universal machine3

Three-tape Deterministic Universal Machine

00010111011011101100110101010100….00….000

tape 1:

current / updated state

tape 2:

string w

tape 3:


Three tape deterministic universal machine4

Three-tape Deterministic Universal Machine

00010111011011101100110101010100….00….000

tape 1:

current / updated state

tape 2:

string w

tape 3:


Three tape deterministic universal machine5

Three-tape Deterministic Universal Machine

00010111011011101100110101010100….00….000

tape 1:

current / updated state

tape 2:

string w

tape 3:


Three tape deterministic universal machine6

Three-tape Deterministic Universal Machine

00010111011011101100110101010100….00….000

tape 1:

current / updated state

tape 2:

string w

tape 3:


Three tape deterministic universal machine7

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!!


Cse355 an introduction to the theory of computer science

CSE355An Introduction to the Theory of Computer Science

Good luck your finals

&

Enjoy your Winter break …


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