1. NP and NP completeness 姚鹏晖
助教: 刘明谋
答疑时间: 周四 2pm-4pm, 计算机科学与技术楼 502

2. What we have learnt
Turing machines: a mathematical model of computational processes.
Church-Turing thesis.
The existence of universal Turing machines.
The existence of uncomputable functions. Halting problem.
The complexity class P, which captures all the problems that are efficiently solvable.
Robustness of the definition of Turing machines.
Strong Church-Turing thesis.

3. Definition of NP

4. Examples in NP

5. Examples in NP

6. Relation between NP and P

7. Deterministic Turing machines

8. Nondeterministic Turing machines

9. Nondeterministic Turing machines

10. Nondeterministic Turing machines

11. Reducibility and NP-Completeness

12. Reducibility and NP-Completeness

13. Reducibility and NP-Completeness

14. Reducibility and NP-Completeness

15. The Cook-Levin Theorem

16. The Cook-Levin Theorem

17. Computation is local ?
It can be verified locally

18. Must accept within p(n) steps.
Variables
interpretation
Numbers
Expression
Interpretation
Numbers
Initial contents of the cells
Initial state of M 1
Initial position of the heads
At most one symbol per cell
At least one symbol per cell
Cells remain unchanged unless written
Only one state at a time
Only one head position at a time
Possible transitions step t when the head of i-th tape is at position j
Must accept within p(n) steps.

19. The Cook-Levin Theorem

20. The Cook-Levin Theorem

23. Examples in NP

24. Examples in NP

25. Decision vs. Search

26. Must accept within p(n) steps.
Variables
interpretation
Numbers
Expression
Interpretation
Numbers
Initial contents of the cells
Initial state of M 1
Initial position of the heads
At most one symbol per cell
At least one symbol per cell
Cells remain unchanged unless written
Only one state at a time
Only one head position at a time
Possible transitions step t when the head of i-th tape is at position j
Must accept within p(n) steps.

27. CoNP

28. NEXP

29. What if P=NP?

30. What if P≠NP?