CS 505 Computability and Complexity Theory
Time and location:
Monday, Wednesday and Friday 2:00-2:50pm, Thomas Beckham Hall (TBH), Room 180E
office hours: TBA
This course discusses fundametal concepts in compatability and complexity theory. The topics covered include models of computation, undecidability, polynomial-time computation and the classes P and NP, diagonalization, space complexity and the classes PSPACE and NL, the polynomial hierarchy, circuit complexity, randomized computation, interactive proofs, cryptography, quantum computation, and hardness of approximation.
The standard prerequisite course is CS 301 or an equivalent one.
The course will also require general mathematical maturity (i.e. the ability to read and write proofs).
No other special background will be necessary.
There will be one midterm, a final exam, and several homeworks.
The final exam will be comprehensive.
Each homework will be due before the beginning of a predetermined lecture.
No late assignments will be accepted.
The final score is computed using the formula: 0.35 × homeworks + 0.3 × midterm + 0.35 × final.
The final letter gades will be curved.
Jan 14, 2019. Lecture 1: Introduction. Turing machines (Chapter 1).
Jan 16, 2019. Lecture 2: Universal Turing machines. Uncomputability (Chapter 1).
Jan 18, 2019. Lecture 3: The classes P and NP (Chapter 2).
Jan 23, 2019. Lecture 4: Polynomial time reductions, NP-completeness (Chapter 2).
Jan 25, 2019. Lecture 5: The Cook-Levin theorem (Chapter 2).
Jan 28, 2019. Lecture 6: Diagonalization. Time and space hierarchies (Chapter 3).
Feb 1, 2019. Lecture 7: Nondeterministic time hierarchy (Chapter 3).
Feb 4, 2019. Lecture 8: Ladner's Theorem. Oracle machines (Chapter 3).
Feb 6, 2019. Lecture 9: Space complexity. PSPACE completeness (Chapter 4).
Feb 8, 2019. Lecture 10: PSPACE-completeness of TQBF. Savitch's theorem (Chapter 4).
Feb 11, 2019. Lecture 11: NL (Chapter 4).