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Example. Trace the following Turing machine for input:#abc# (the head initially points to the first blank on the right-hand-side) Start Lr action description Input/output string Start #abc#(there are more# on the right-hand-side →Lr move the head to the first # on left #abc## →Rr move head one letter to right #abc## The head is pointing at #abc## a, so r=a. follow → # Replace a with # ##bc## →Rr move the head to first # on ##bc##, right(there are more # on right) →Rr r and replace it with r=a (more # on right) ##bc#a_# Lr move to the first # on left, ##bc#a# Lr# r, and move to the next blank on left agian(together means move to the 2nd blank on left)and replace it with r =a. before we go back to the loop, all we did so far is to put a copy of 'a' on the right hand side #abc#a# R→# Move head to right, r=b which is not blank. Replace it with # #a#c#a# Rrb r Lets do all at once. Move to the second blank on right and replace # with r=b #a#c#ab# LrLr r, Move to the second blank on Left, and replace the # with r=b #abc#ab# R→ # Move the head to Right, r=c not blank. Replace c with # t #ab##ab# Rrc r Move to the second blank on right and replace # with r=c #ab##abc# LrLr r, Move to second blank on left and replace it with r=c #abc#abc# R Move head to right, the box is # #abc#abc# Rr Move head to first # on right #abc#abc# In summary, this machine used the input string #abc# to produce output #abc#abc#. Thus, the input string #w# creates output string #w#w#, or word w followed by its copy. We name this machine a COPY machine or C, and from now on you can use it when you need it. Notation. Since #w# was the input to the Turing machine and #w#w# was its output, we use function notation to describe its action. If the function name be f, then

          Example. Trace the following Turing machine for input:#abc# (the head initially points to the first blank on the right-hand-side)
Start L<sub>r</sub>
action
description
Input/output string
Start
#abc#(there are more#
on the right-hand-side
→L<sub>r</sub>
move the head to the first # on left
#abc##
→R<sub>r</sub>
move head one letter to right
#abc##
The head is pointing at
#abc##
a, so r=a.
follow → #
Replace a with #
##bc##
→R<sub>r</sub>
move the head to first # on
##bc##,
right(there are more # on right)
→R<sub>r</sub> r
and replace it with r=a (more # on right)
##bc#a_#
L<sub>r</sub>
move to the first # on left,
##bc#a#
L<sub>r</sub># r,
and move to the next blank on left agian(together means move to the 2<sup>nd</sup> blank on left)and replace it with r =a. before we go back to the loop, all we did so far is to put a copy of 'a' on the right hand side
#abc#a#
R→#
Move head to right, r=b which is not blank. Replace it with #
#a#c#a#
R<sub>r</sub>b r
Lets do all at once. Move to the second blank on right and replace # with r=b
#a#c#ab#
L<sub>r</sub>L<sub>r</sub> r,
Move to the second blank on Left, and replace the # with r=b
#abc#ab#
R→ #
Move the head to Right, r=c not blank. Replace c with # t
#ab##ab#
R<sub>r</sub>c r
Move to the second blank on right and replace # with r=c
#ab##abc#
L<sub>r</sub>L<sub>r</sub> r,
Move to second blank on left and replace it with r=c
#abc#abc#
R
Move head to right, the box is #
#abc#abc#
R<sub>r</sub>
Move head to first # on right
#abc#abc#
In summary, this machine used the input string #abc# to produce output #abc#abc#. Thus, the input string #w# creates output string #w#w#, or word w followed by its copy. We name this machine a COPY machine or C, and from now on you can use it when you need it.
Notation. Since #w# was the input to the Turing machine and #w#w# was its output, we use function notation to describe its action. If the function name be f, then

example trace the following turing machine for inputabc the head initially points to the first blank on the right hand side start lsubrsub action description inputoutput string start abcther 49061

Added by Elizabeth W.

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