The document discusses Turing machine programming techniques, particularly methods for recognizing the left end of the tape and building Turing machines for specific languages like 0n 1n 0n. It describes the use of special symbols to facilitate string comparison and the possibility of non-destructive replacements to preserve original strings. Key examples are given, illustrating how to create larger machines by combining simpler ones.

1. TOPIC
Turing Machine
Programming Techniques

2. Group Member
Basit Hussain 2017 – CS- 126
Hamza 2017 – CS- 105
Irtiza 2017 – CS- 126
Minhaj Wajid 2017 – CS- 051
Muhammad Umer Khan 2017 – CS- 027

3. Tu r i n g M a c h i n e P r o g r a m m i n g Te c h n i q u e s
Problem: How can we recognize the left end of the tape of a Turing machine?
Solution: Put a Special Symbol $ on the left end of the Tape and shift the
input over one cell to the right
a a a b b a ….
a a a b b a ….$

4. Tu r i n g M a c h i n e P r o g r a m m i n g Te c h n i q u e s
over one cell to the right.
a a a b b a ….
a a a b b a ….$
D
B
C
A
a $, R
a a, R
a, L
$ $, R
b $, R
a b, R b a, R
a a, L
b b, L
b, L
b b, R

5. Tu r i n g M a c h i n e P r o g r a m m i n g Te c h n i q u e s
Example: Building a Turing Machine to recognize the language 0N 1N 0N
We already hava a Turing Machine to turn 0N 1N to XN YN and to decide
that language.
USE THIS TURING MACHINE AS A SUBROUTINE
IDEA

6. Tu r i n g M a c h i n e P r o g r a m m i n g Te c h n i q u e s
Example: Building a Turing Machine to recognize the language 0N 1N 0N
Step 1: 0 0 0 0 1 1 1 1 0 0 0 0
x x x x y y y y 0 0 0 0
Step 2: Build a similar Turing Machine to recognize yN 0N
Step 3: Build a final Turing Machine combining these two smaller
Turinng Machine together into one larger Turing Machine

7. Tu r i n g M a c h i n e P r o g r a m m i n g Te c h n i q u e s
Comparing Two Strings
A Turing Machine to decide { w # w | w E {a, b, c}*}
Solution:
• Use a new Symbol such as ‘x’.
• Replace each Symbol into an x after it has been examined.

8. Tu r i n g M a c h i n e P r o g r a m m i n g Te c h n i q u e s
Solution:
• Use a new Symbol such as ‘x’.
• Replace each Symbol into an x after it has been examined.
a b b a c # a b b a c
x b b a c # a b b a c
x x b a c # a b b a c
x x x c # a b b a c
a b x a c # a b b a c
a b b a c # a b b a c
We lost the original
String

9. Tu r i n g M a c h i n e P r o g r a m m i n g Te c h n i q u e s
Problem:
Can we do its non-destructively? i.e without losing the original strings?
Solution:
Replace each unique symbol with another unique symbol instead of replacing
all with the same symbol.
a b b a c # a b b a c
p q q p r # p q q p r
Restore the original string if required