The document discusses Turing machines, which can be both logical and physical devices. A Turing machine uses a tape like an infinite array and can read/write to cells on the tape and move left/right. It has a finite set of states and transition functions. Several examples are provided of designing Turing machines to perform tasks like reversing a binary number, checking for palindromes, and swapping all 'a's and 'b's in a string. In conclusion, Turing machines are an important theoretical model of computation that later inspired actual computer hardware.

1. Turing Machine
by:ArwaWshear& Exllass Fread
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2. What is Turing Machine?
So what is Turing Machine ?
Is it some physical machine ?
Or some sort of imaginary machine ?
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3. The answer:
The answer is it’s both logical and
physical device!!!
The Turing machine can be logical device then we
convert it to physical device one example we
can create a TM that reverse a string
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4. A physical Turing Machine
Here I will show you an actual Turing machine
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5. Lets get started
Every machine have an input and an output between the input and
output there is process
The input to any TM is just a String
The process here we will create it according to our need later we will
see how to design it
The Output is also a string 5

6. Our goal ?
Our goal in designing any Turing machine is to implement our idea
in term of states and transitions so we need to know about our
recourses but before that
State State
Transitions
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7. Our recourses
The only recourse that we have is long tape its exactly like an array
But how we can use this tape ?
For every game we have set of rules here also just like a gameI tells you ,
you can use this tape so design this for me
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8. The rules
1- you can read cell by cell
2- you can change the content of the cell
3- you can move to the right or to the left
4- you can use as much as you want from the tape its like infinite storage
store as elements as you wish
Here is what you can do with this tape
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9. You cannot do this
You can not do this things in our game
1- you cannot jump form a cell to a far cell just cells next to each other
2- we will give you set of thing you can use them only as
input to our machine
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10. Structure of Turing Machine
Finite state control
Read/Write head
We can read or write any symbol
that we like
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11. TM= {Q,┌,b, ∑,δ ,q_0, F}
Q : is a finite, non-empty set of states
┌ : is a finite, non-empty set of the tape alphabet/symbols
∑ : is the set of input symbols
q_0 : is the initial state
F : is the set of final or accepting states.
δ : called the transition function, where L is left shift, R is right shift.
B : is the blank symbol (the only symbol allowed to occur on the tape
infinitely often at any step during the computation)
Formal Definition of Turing Machine
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12. Some Examples
Ex/ Design a TM to that output is a 1's complement of a binary
number
Solution:
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13. The Solution δ 𝑞0, 0 = δ 𝑞0, 1, 𝑅
δ 𝑞0, 1 = δ 𝑞0, 0, 𝑅
δ 𝑞0, 𝐵 = δ 𝑞0, 𝐵, 𝐻
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14. Some Examples
Ex2: design the Turing Machine to accept the palindrome string ex:
aaa , abba , abaaba .........
Solution :
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15. The Solution
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δ 𝑞0, a = δ 𝑞1, A, 𝑅
δ 𝑞1, 𝑎 = δ 𝑞1, a, 𝑅
δ 𝑞1, b = δ 𝑞1, b, 𝑅
δ 𝑞1, b = δ 𝑞3, b, 𝑅
δ 𝑞3, = δ 𝑞0, 1, 𝑅
δ 𝑞0, 0 = δ 𝑞0, 1, 𝑅
δ 𝑞0, 0 = δ 𝑞0, 1, 𝑅
δ 𝑞0, 0 = δ 𝑞0, 1, 𝑅
δ 𝑞0, 0 = δ 𝑞0, 1, 𝑅
δ 𝑞0, 0 = δ 𝑞0, 1, 𝑅
δ 𝑞0, 0 = δ 𝑞0, 1, 𝑅
δ 𝑞0, 0 = δ 𝑞0, 1, 𝑅
δ 𝑞0, 0 = δ 𝑞0, 1, 𝑅
δ 𝑞0, 0 = δ 𝑞0, 1, 𝑅
δ 𝑞0, 0 = δ 𝑞0, 1, 𝑅
δ 𝑞0, 0 = δ 𝑞0, 1, 𝑅
δ 𝑞0, 0 = δ 𝑞0, 1, 𝑅
δ 𝑞0, 0 = δ 𝑞0, 1, 𝑅
δ 𝑞0, 0 = δ 𝑞0, 1, 𝑅
δ 𝑞0, 0 = δ 𝑞0, 1, 𝑅

16. Some Examples
Ex3/ create a turing machine for (a ∪ b) ∗aa
Solution:
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17. The Solution δ 𝑞0, 𝐵 = δ(𝑞1, 𝐵, 𝑅)
δ 𝑞1, 𝑏 = δ(𝑞1, 𝑏, 𝑅)
δ 𝑞1, 𝑎 = δ(𝑞2, 𝑎, 𝑅)
δ 𝑞2, 𝑏 = δ(𝑞1, 𝑏, 𝑅)
δ 𝑞2, 𝑎 = δ(𝑞3, 𝑎, 𝑅)
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18. Some Examples
EX4 /create a turing machine to Swap all a’s to b’s and all b’s to a’s in a string of a’s and b’s
TM= {{𝑞0,𝑞1,𝑞2,𝑞3},{a,b},{a,b,B,x,y},δ ,𝑞2}
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19. The Solution
δ 𝑞0, 𝐵 = δ(𝑞1, 𝐵, 𝑅)
δ 𝑞1, 𝑏 = δ(𝑞1, 𝑎, 𝑅)
δ 𝑞1, 𝑎 = δ(𝑞1, 𝑏, 𝑅)
δ 𝑞1, 𝐵 = δ(𝑞2, 𝐵, 𝐿)
δ 𝑞2, 𝑎 = δ(𝑞2, 𝑎, 𝐿)
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20. Conclusion
TM is important term or idea in computer science or computer
technology it’s about idea and mind TM is used in our computer phones
or at least its idea, When Alan Turing invite this new (Idea or Device) his
idea was to create something capable of solving everything that can be
solved on this idea universal TM appeared if we have something that
can compute everything computable
Logically we must have something that can simulate TM itself and this
thing is UTM
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21. References
1.princeton.2013 http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Non-deterministic_Turing_machine.html
2.Ed Gonzales .2013 http://stackoverflow.com/questions/236000/whats-a-turing-machine
3.Brunfiel , Geoff, Student snags maths prize, Nature, October 24. 2007.
4.Alasdair Urquhart, 2007 "Smallest universal machine", FOM email list. October 26, 2007.
5.A. Salomaa , "Formal languages" , Acad. Press (1973)
6.T. Pajor , "A Deterministic Turing Machine that Accepts Primes", Universität Karlsruhe (2004)
7.S. Eilenberg , "Automata, languages and machines" , A , Acad. Press (1974)
8.A. Salomaa, M. Soittola , "Automata-theoretic aspects of formal power series" , Springer (1978)
* including our lecture and several lectures from other universities
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22. That is all …….
Thanks for You
Arwa…Exllass…
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