G22.3033-002 Computational Complexity Subhash Khot

Spring 2009

---

General Information and Announcements

Keep looking for updates. It is your responsibility to watch out for announcements regarding homeworks, exams, handouts etc. No emails will be sent.

Homework 3 and take-home end-term are now online. Both due on May 4.

A list of candidate course projects.

---

Prerequisites

Prior knowledge of following materials is assumed. A brief overview of basics will be given in the first lecture. Other than this, the course should be self-contained.

• Discrete math and probability.
• Data structures : lists, trees, stacks etc.
• Algorithms, asymptotic running time, basic algorithms like breadth/depth-first search, sorting etc.
• Finite automata (deterministic and non-deterministic), regular languages, context free languages.
• Turing machines, decidability, NP-completeness, reductions.

References for this basic material are :

• M. Sipser : Introduction to the theory of computation.
• T. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein : Introduction to Algorithms (Second Edition).

---

Administrative Information

Lectures: Mon 7:10-9:00, WWH 312

Professor: Subhash Khot – WWH 416 , 212-998-4859, Office hours : Mon 6-7 pm.

---

Course Syllabus

The first part of the course will cover basic aspects of complexity theory. This includes complexity classes P, NP, L, NL, PSPACE, Polynomial Hierarchy, BPP, P/poly, NC, IP, AM, #P and relationships among them.

The second part of the course will cover advanced toipcs, e.g. PCPs, circuit lower bounds, communication complexity, derandomization, property testing and quantum computation. The emphasis will be on breadth rather than covering any of these topics in depth. We will introduce a specific topic, give a broad overview of results, and only a glimpse of the techniques. During this part of the course, you would need to read a couple of advanced research papers/surveys and write a report.

---

Homeworks and Exams

• Homework 1 Due March 9

• Homework 2 Due March 16

• Midterm Due March 30

• Homework 3 Due May 4

• Endterm Due May 4

---

References and Textbooks

We will not "follow" any particular textbook. You may want to refer to :

• C.H. Papadimitriou : Computational Complexity.
• D.Z. Du and K.I. Ko : Theory of Computational Complexity.

Course notes from similar courses taught at Princeton and UC-Berkeley would be useful. See :

• Sanjeev Arora's Spring 2003 course at Princeton.
• Luca Trevisan's notes from Fall 2002 course at UC-Berkely.

---