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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
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
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 tm1
3.1 Turing machines (TM)
  • Turing machine have both accept and reject states.
  • Turing machine is unlike the PDA in:

FA part

(state diagram)

Tape Head (Read\Write)

W string + blank

Input tape (infinite memory )

Computer Science Department

3 1 turing machines tm2
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 tm3
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
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 tm1
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
  • What about if ??

Computer Science Department

Computer Science Department

formal definition of tm2
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 tm3
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
TM – example’s

Computer Science Department

Computer Science Department

tm example s1
TM – example’s
  • Give the formal definition to M2

Computer Science Department

Computer Science Department

tm example s2
TM – example’s
  • The formal definition of M2 is:

Computer Science Department

Computer Science Department

tm example s3
TM – example’s
  • Run input string 0000 on M2:

Computer Science Department

Computer Science Department

tm example s4
TM – example’s

Computer Science Department

Computer Science Department

tm example s5
TM – example’s

Computer Science Department

Computer Science Department

tm example s6
TM – example’s

Computer Science Department

Computer Science Department

tm example s7
TM – example’s

Computer Science Department

Computer Science Department

tm example s8
TM – example’s
  • Let M be the TM defined by:

Computer Science Department

Computer Science Department