Chapter 3 : The CHURCH-Turing thesis

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# Chapter 3 : The CHURCH-Turing thesis - PowerPoint PPT Presentation

CS314: Formal languages and automata theory L. Nada ALZaben. Chapter 3 : The CHURCH-Turing thesis. Quick Note. don’t forget to read chapter 2 section 2 .1 and 2 .2 Always check the blog for new updates: Cs314pnu.wordpress.com. 3.1 Turing machines (TM). Lecture # 11.

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Quick Note
• don’t forget to read chapter 2section 2.1 and 2.2
• Always check the blog for new updates:

Cs314pnu.wordpress.com

Computer Science Department

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

3.1 Turing machines (TM)
• Turing machine have both accept and reject states.
• Turing machine is unlike the PDA in:

FA part

(state diagram)

W string + blank

Input tape (infinite memory )

Computer Science Department

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 } ….(imagine your self as M1)

Computer Science Department

Computer Science Department

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 } ….(imagine your self as M1)

Computer Science Department

Computer Science Department

Formal definition of TM
• Most thing need to be known is the transition function ( ᵟ) which is described as (ᵟ is deterministic)

Computer Science Department

Computer Science Department

Formal definition of TM
• Halt state.
• Configuration of TM (the status of the machine is a setting of three items) e.g.
• We say configuration C1 yields configuration C2 if the TM can change from C1 to C2 by one single step.
• E.g. yields

Computer Science Department

Computer Science Department

Formal definition of TM
• Configuration states may be:
• In the start configuration the state is
• In the Accept configuration the state is
• In the Reject configuration the state is
• Accept configuration and Reject configuration are halting configuration

Computer Science Department

Computer Science Department

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

Computer Science Department

TM – example’s

Computer Science Department

Computer Science Department

TM – example’s
• Give the formal definition to M2

Computer Science Department

Computer Science Department

TM – example’s
• The formal definition of M2 is:

Computer Science Department

Computer Science Department

TM – example’s
• Run input string 0000 on M2:

Computer Science Department

Computer Science Department

TM – example’s

Computer Science Department

Computer Science Department

TM – example’s

Computer Science Department

Computer Science Department

TM – example’s

Computer Science Department

Computer Science Department

TM – example’s

Computer Science Department

Computer Science Department

TM – example’s
• Let M be the TM defined by:

Computer Science Department

Computer Science Department