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Chapter 3 : The CHURCH-Turing thesis

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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Chapter 3 : The CHURCH-Turing thesis

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

  2. 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. 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. 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

  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 } ….(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 } ….(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) Computer Science Department 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. • 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

  9. 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

  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 Computer Science Department

  11. TM – example’s Computer Science Department Computer Science Department

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

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

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

  15. TM – example’s Computer Science Department Computer Science Department

  16. TM – example’s Computer Science Department Computer Science Department

  17. TM – example’s Computer Science Department Computer Science Department

  18. TM – example’s Computer Science Department Computer Science Department

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

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