CS 710 - Complexity Theory
This course provides a graduate-level introduction to computational complexity
theory, the study of the power and limitations of efficient computation.
In the first part of the course we focus on the standard setting, in which one
tries to realize a given mapping of inputs to outputs in a time- and
space-efficient way. We develop models of computation that represent the
various capabilities of digital computing devices, including parallelism,
randomness, quantum effects, and nonuniformity. We also introduce models
based on the notions of nondeterminism, alternation, and counting, which
precisely capture the power needed to efficiently compute important types
of mappings. The meat of this part of the course consists of intricate
relationships between these models, as well as some separation results.
In the second part, depending on the interest of the students, we may
study other computational processes that arise in
diverse areas of computer science, each with their own relevant efficiency
measures. Specific possible topics include:
- proof complexity, interactive proofs, and probabilistically checkable
proofs -- motivated by verification,
- pseudorandomness and zero-knowledge -- motivated by cryptography and
- computational learning theory -- motivated by artificial intelligence,
- communication complexity -- motivated by distributed computing,
- query complexity -- motivated by databases.
Complexity theory at the level of CS 520. We will start the course with
a quick review of the relevant CS 520 material. If you haven't taken
CS 520 or an equivalent course before but are mathematically mature,
you should be able to pick up the prerequisite material from the review.
There is no required text.
Lecture notes will be made available from the course web page.
Relevant references are the text books
A Modern Approach by Sanjeev Arora and Boaz Barak, and
Complexity: A Conceptual Perspective by Oded Goldreich.
MWF 2:30-3:45pm in 1325 CS&S. On average only 2 of the 3 weekly
slots will be used.
- Homework (40%).
There will be 2 assignments. You should work on the assignments in pairs.
- Paper Presentation (60%).
Read a recent paper on computational complexity and present it to the
Dieter van Melkebeek.
Office hours: F 4-5pm and by appointment.