Recent advances in the study of Complexity (Sitharam)

CIS 6930/CIS 4930, Fall 2002.

Time and Place

Tues 5th and 6th periods and Thurs 6th period. Room CBD 324 in Building 105 (behind Burger King).

Description of the course.

This course would cover many of the recent, exciting advances in complexity theory, from traditional computational complexity, including alternative models and measures of complexity, from physical and biologically inspired models and measures to abstract mathematical (noncomputational) measures of complexity. There will be a tendency towards a geometric treatment with some algebraic techniques thrown in, although purely combinatorial techniques will also be prevelant. Any required background beyond an algorithms or theory of computation class will be covered, or explicit reading material will be provided.

NOTE: Click here for Dr. Sitharam's papers on complexity theory, particularly the (NP.vs. Co-NP) and (P vs. BPP) themes (see below).

Format of the course:

This is a standard course format followed by special topics theory courses in many schools. I will pick 6-7 results and corresponding sets of accessible papers or book chapters and compile all of the material that is necessary to build up all of the background (beyond an algorithms or theory of computation class) needed to explain them. Each set of papers will have a student(s) assigned to it. (Each student may get assigned to more than 1 such set). These students will work WITH ME to prepare the lectures for the corresponding weeks; present some lectures; prepare the prior reading material and lecture notes and exercises to post on the website for the class; and finally help grade the returned solutions.

Grading Scheme:

Your grade will be based on: 70% your performance on various tasks related to the the topics assigned to you as described above; 30% on your solutions to the exercises as well as class participation.

Schedule

Week Topic Theme Student Presentation Designated Scribe Reading material Lecture notes
Aug 27 Circuit Size (Lower Bounds) P vs NP None Andrew Here Here and Here
Sep 3 Circuit Size (Lower Bounds) None Andrew Here and Here
Sep 10 Circuit Size (Lower Bounds) None Zia Here and Here
Sep 17 Circuit Size(Lower Bounds) Zia Zia Here and Here
Sep 24 Circuit Size (Lower Bounds) None Zia Here and Here
Oct 1 Circuit Depth (Lower Bounds) None Erwin Here and Here
Oct 8 Circuit Depth(Lower bounds) Proof technique limitations None Erwin Here and Here
Oct 15 Circuit Depth/Natural Proofs Erwin Erwin Here and Here
Oct 22 Natural Proofs Erwin Henry Here Here and Here
Oct 29 Pseudorandomness P vs. BPP None Henry Here Here
Nov 5 Derandomization None Henry Here and Here
Nov 12 Derandomization None Srijit Here and Here
Nov 19 Derandomization None Srijit Here and Here (continued in the Nov 26 lecturenotes)
Nov 26(1/2) Physics Information Computation Alt. Models Srijit Srijit Here Here
Dec. 3 Quantum Computation Srijit/Henry Srijit/Henry Here Here Here and Here (continued on Dec 10)
Dec 10 (1/2) Biogeometric Models of Computation Henry/Andrew Henry/Andrew Here Here and Here

Deadlines for scribes: notes are due by the end of Thursday, and should be in Dr. Sitharam's mailbox on Friday morning. Coordinate by on Friday morning by email with Dr. Sitharam, so that any corrections can be communicated to you over the weekend.

Deadlines for speakers: you should meet Dr. Sitharam on Monday, 3PM, 2 weeks before your talk to obtain papers and again next Monday to discuss your presentation. This will generally be moved to 4pm if the amount of anticipated discussion is not large, and if only one student is to meet. If 2 students are to meet Dr. Sitharam on the same day, one will meet at 3 and one at 4. Please contact Dr. Sitharam well in advance.

Deadlines for turning in HW exercises: by 3 wks after day assigned.

Here is the template Latex file for scribes sample.tex as well as the preamble.tex . Save both files in the same directory, lecture notes should go in sample.tex, do not modify preamble.tex unless you really want to.