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Course Professors: Sam Buss, Russell Impagliazzo, Mohan Paturi.

**Meeting times for Winter 2013: Tuesdays, 11:00-12:30, APM 6218.**

This will be a reading and discussion seminar course devoted to understanding some core results in sublinear space.

**Please sign up for the
piazza.com roster for the course**.
(We are still using the Fall 2012 piazza.com pages.)
The piazza.com pages will be used for posting announcements about the schedule;
it may optionally be used for online discussion about course topics as well.

If you need a piazza.com invitation, email at Sam at sbuss@math.ucsd.edu.

Students who are actively attending are encouraged to sign up for one unit of credit.

The handwritten lectures or scribe notes are completely rough, unproofread, and unedited. They are intended to serve as an informal record of what might have been presented during the lecture. Caveat lector!

**January 15, 2013.**
Introductory topics overview,
lecture by Sam Buss.
*Sam's handwritten lecture notes.*

**January 22, 2013.**
Reversible computation.
Lecture by Sam Buss.
*Sam's
handwritten lecture notes.*

- [1] C.H. Bennett, "Logical Reversibility of Computation", IBM J. Res. Develop., 17 (1973) 525-532. PDF
- [2] C.H. Bennett, "Time-Space Trade-off for Reversible Computation", SIAM J. Computing, 18 (1989) 766-776. PDF [3] R.Y. Levine and A.T. Sherman, "A Note on Bennett's Time-Space Tradeoff for Reversible Computation", SIAM J. Computing, 19 (1990) 673-677. PDF
- [4] K.J. Lange, P. McKenzie, and A. Tapp, "Reversible Space Equals Deterministic Space", JCSS 60 (2000) 354-367. PDF
- [5] H. Buhrman, J. Tromp, and P. Vitanyi, "Time and Space Bounds for Reversible Computation", J. Phys. A: Math. Gen. 34 (2001) 6821-6830. PDF
- [6] R. Williams, "Space-Efficient Reversible Simulations", unpublished. PDF

**January 29, 2013.**
USTCON is in RLP: Undirected st-connectivity is in randomized
polynomial time, log space.
Lecture by Sam Buss.
*Sam's handwritten lecture notes.*

- [1] R. Aleliunas, R.M. Karp, R.J. Lipton, L. Lovazs, C.W. Rackoff, "Random Walks, Universal Travelling Sequences, and the Complexity of Maze Problems", 20th STOC, 1979, 218-223.
- [2] R. Motwani and P. Paghavan, "Randomized Algorithms", Cambridge Univ. Press, 1995. Chapter 6.

**February 5 and 12, 2013.**
Pseudorandomness for space bounded computation.
Lectures by Russell Impagliazzo.
*Sam's handwritten scribe notes.*

- [1] N. Nisan, "Pseudorandom Generators for Space-Bounded Computation", Combinatorica 12, 4 (1992) 449-461. PDF
- [2] N. Nisan and D. Zuckerman, "Randomness in Linear in Space", JCSS 52, 1 (1996) 43-52. PDF

**February 19 and 26, and March 5, 2013.**
"Expander graphs and SL=L (Reingold's Theorem)".
Lectures by Sam Buss.
*Sam's
handwritten lecture notes (MORE TO COME)*.