1. How does the Savitch theorem relate to space complexity classes?
2. What is the class APX, and how does it relate to approximability in optimization problems?
3. How do approximation-preserving reductions work in complexity theory?
4. What is the significance of self-reducibility in NP-complete problems?
5. How do fixed-parameter tractability and kernelization relate to complexity classes?
6. What is the role of W-hierarchy in parameterized complexity theory?
7. How do you define a problem as fixed-parameter tractable (FPT)?
8. What is the significance of kernelization in parameterized complexity?
9. How do approximation algorithms handle NP-hard problems in TOC?
10. What is the importance of gap problems in complexity theory?
11. How does the class AM (Arthur-Merlin) extend interactive proofs?
12. What is the significance of space complexity classes like L and NL?
13. What is the importance of log-space transducers in complexity theory?
14. How does the polynomial-time hierarchy affect computational problem classification?
15. What is the role of the class Σ2P in the polynomial-time hierarchy?
16. What is the significance of randomized reductions in complexity theory?
17. How do hardness and completeness interact in the polynomial-time hierarchy?
18. How do you determine if a problem belongs to a higher complexity class like ΣkP?
19. What is the impact of alternating quantifiers in computational complexity?
20. What is the significance of interactive proofs with bounded communication in TOC?
21. What is the class BPL (Bounded-error probabilistic log-space), and how does it relate to L?
22. How does the class NL-complete differ from NL-hard in complexity theory?
23. What is the relationship between randomized algorithms and approximation algorithms?
24. What is the role of derandomization in complexity classes like RP and BPP?
25. How does the class co-RP differ from RP in probabilistic complexity?
26. What is the significance of logarithmic space in Turing machine computation?
27. How does NL relate to PSPACE in space-bounded computation?
28. What are the implications of unbounded-error probabilistic classes like PP?
29. How do you reduce problems in NP-complete classes to other complexity classes?
30. What is the importance of log-space complexity in real-world computation?
31. What is the relationship between the class PSPACE and the polynomial hierarchy?
32. How do interactive proofs generalize NP-completeness in complexity theory?
33. How does error-correction affect the complexity of communication protocols?
34. What is the impact of parallel computation on space complexity classes?
35. How does randomized computation affect the efficiency of parallel algorithms?
36. What is the role of Boolean functions in complexity classes like NC and P?
37. How do you relate space complexity to circuit depth in NC-completeness?
38. What is the significance of Boolean formula complexity in TOC?
39. How do completeness and approximation interact in NP-hard problems?
40. What is the significance of interactive proofs in higher complexity classes?