Chapter 3 : The CHURCH-Turing thesis

Chapter 3: The CHURCH-Turing thesis

CS314: FORMAL LANGUAGES AND AUTOMATA THEORYL. NADA ALZABEN

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Quick Note don’t forget to read

chapter 2section 2.1 and 2.2

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Computer Science Department

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3.1 Turing machines (TM) 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.


Lecture #11

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Turing machine have both accept and reject states.

Turing machine is unlike the PDA in:

Input tape (infinite memory )

Tape Head (Read\Write)

FA part (state diagram)

W string + blank

3.1 Turing machines (TM)



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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)



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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)



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Formal definition of TM Most thing need to be known is the transition

function ( ᵟ) which is described as (ᵟ is deterministic)



8 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 What about if ??

Formal definition of TM



9 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



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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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TM – example’s



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Give the formal definition to M2

TM – example’s



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



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



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TM – example’s



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TM – example’s



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TM – example’s



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TM – example’s



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


Chapter 3 : The CHURCH-Turing thesis

Documents

computer science department23

turing machines tmwe

churchturing thesiscs314

powerful models alan

automata unlimited memory

formal languages

unrestricted memory

automata theoryl