CS 505 Computability and Complexity Theory
Spring, 2019
Time and location:
Monday, Wednesday and Friday 2:002:50pm, Thomas Beckham Hall (TBH), Room 180E
Intructor:
Anastasios Sidiropoulos,
sidiropo@uic.edu,
office hours: TBA
Overview
This course discusses fundametal concepts in compatability and complexity theory. The topics covered include models of computation, undecidability, polynomialtime 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.
Textbooks
Evaluation
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.
Lectures

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, NPcompleteness (Chapter 2).

Jan 25, 2019. Lecture 5: The CookLevin 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: PSPACEcompleteness of TQBF. Savitch's theorem (Chapter 4).

Feb 11, 2019. Lecture 11: NL (Chapter 4).