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
مکمل گیری

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: