1. Chapter 3: The CHURCH-Turing thesis
CS314: Formal languages and automata theory L. Nada ALZaben
Chapter 3: The CHURCH-Turing thesis

2. Quick Note don’t forget to read chapter 2section 2.1 and 2.2
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3. 3.1 Turing machines (TM)
Lecture #11
We have presented in previous lectures the Finite Automata model (small amount of memory) and Push Down Automata ( unlimited memory with the concept of last in first out.
But they do not serve as models of general purpose computers.
Turing machines are powerful models (Alan Turing- 1936). It is similar to FA but with unlimited and unrestricted memory.
Turing machine is more accurate model of general purpose computer.
Computer Science Department

4. Tape Head (Read\Write)
3.1 Turing machines (TM)
Input tape (infinite memory )
Tape Head (Read\Write)
FA part
(state diagram)
W string + blank
Turing machine have both accept and reject states.
Turing machine is unlike the PDA in:
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5. 3.1 Turing machines (TM)
E.g. M1 is a machine that will accept if the string is a member of B={w#w |w ∈ {0,1} ∗ } ….(imagine your self as M1)
Computer Science Department
Computer Science Department

6. 3.1 Turing machines (TM)
E.g. M1 is a machine that will accept if the string is a member of B={w#w |w ∈ {0,1} ∗ } ….(imagine your self as M1)
Computer Science Department
Computer Science Department

7. Formal definition of TM
Most thing need to be known is the transition function ( ᵟ) which is described as (ᵟ is deterministic)
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Computer Science Department

8. Formal definition of TM
Halt state.
Configuration of TM (the status of the machine is a setting of three items) e.g. 𝒖𝒒𝒗
We say configuration C1 yields configuration C2 if the TM can change from C1 to C2 by one single step.
E.g. 𝒖𝒂 𝒒 𝒊 𝒃𝒗 yields 𝒖 𝒒 𝒋 𝒂𝒄𝒗 𝒊𝒇 𝜹 𝒒 𝒊 ,𝒃 = 𝒒 𝒋 , 𝒄,𝑹 .
What about if 𝜹 𝒒 𝒊 ,𝒃 = 𝒒 𝒋 , 𝒄,𝑳 ??
Computer Science Department
Computer Science Department

9. Formal definition of TM
Configuration states may be:
In the start configuration the state is 𝒒 𝟎 𝒘
In the Accept configuration the state is 𝒒 𝒂𝒄𝒄𝒆𝒑𝒕
In the Reject configuration the state is 𝒒 𝒓𝒆𝒋𝒆𝒄𝒕
Accept configuration and Reject configuration are halting configuration
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Computer Science Department

10. Formal definition of TM
Loop means the TM never halt.
TM are deciders if they halt on every input (never loop) (less time waiting)
Every Turing-decidable is Turing-recognizable but not vice versa
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11. TM – example’s
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Computer Science Department

12. TM – example’s Give the formal definition to M2
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Computer Science Department

13. TM – example’s The formal definition of M2 is:
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Computer Science Department

14. TM – example’s Run input string 0000 on M2:
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Computer Science Department

15. TM – example’s
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Computer Science Department

16. TM – example’s
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Computer Science Department

17. TM – example’s
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Computer Science Department

18. TM – example’s
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Computer Science Department

19. TM – example’s Let M be the TM defined by: Computer Science Department