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Language Theory and Turing Machines

A comprehensive guide to language theory and Turing machines, covering topics such as decidability, recognizability, complement languages, and more.

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Language Theory and Turing Machines

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  1. ماشین های تورینگ، تشخیص پذیری و تصمیم پذیری زبان ها جلسات حل تمرین نظریه زبان ها و ماشین ها دانشگاه صنعتی شریف بهار 87

  2. Enumerators • Show that a language is decidable iff some enumerator enumerates the language in lexicographic order. • Show that every infinite recognizable language has an infinite decidable language as a subset.

  3. طراحی تصمیم گیر

  4. زبان های مکمل-تشخیص پذیر(co-recognizable)

  5. زبان های تصمیم پذیر

  6. زبان های تصمیم پذیر M is a Turing machine • Does M take more than k steps on input x? • Does M take more than k steps on some input? • Does M take more than k steps on all inputs? • Does M ever move the tape head more than k cells away from the starting position?

  7. زبان های تصمیم پذیر • {M: M is the description of a Turing machine and L(M) is a Turing recognizable language}

  8. زبان های تصمیم ناپذیر

  9. زبان های تشخیص ناپذیر

  10. زبان های تشخیص ناپذیر Consider the following language L: L = { <M> | for every input string w, M will halt within 1000|w|2 steps } Show that this language is not recognizable. (Reduce from ~ATM.) complement of

  11. طراحی تشخیص دهنده

  12. Close look to the formal definition of a TM • Exercise 3.5: • Can a Turing machine ever write the blank symbol on its tape? • Can the tape alphabet be the same as the input alphabet? • Can a Turing machine's read head ever be in the same location in two successive steps? • Can a Turing machine contain just a single state?

  13. خواص بسته بودن • زبان های تشخیص پذیر: • اجتماع • اشتراک • تکرار(*) • الحاق • زبان های تصمیم پذیر • اجتماع • اشتراک • مکمل گیری • تکرار(*) • الحاق

  14. Robustness • doubly infinite tape • k-stack PDAs (k>1) • A Turing machine with only RIGHT and RESET moves • Cyclical Turing machine • A queue automaton • 2(k) head Turing machine • Turing machine with k-dimensional tape • A single tape TM not allowed to change the input -> regular language • Only Right and Stay Put moves -> regular language

  15. Clue to the Solution: input-read-only TM At most the last |Q| squares of input on tape can be determining. Myhill-Nerode theorem • if a language L partitions ∑* into a finite number of equivalence classes then L is regular. • See: http://www.eecs.berkeley.edu/~tah/172/7.pdf http://en.wikipedia.org/wiki/Myhill-Nerode_theorem

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