Ph.D. University of California, Berkeley, 1990
My research interests include computational complexity and randomized
computation. In particular, I have been working in the area of program
correctness. The study of program checkers, self-testing programs, and
self-correcting programs is a new approach to ensuring the correctness
of program results. The key idea is to allow one to use a program to
compute a function without having to trust a priori that it works
correctly. This is accomplished by having a checker determine whether
the program gives the correct answer on a particular input. Our work
has introduced two new concepts useful to the development of such
checkers: a self-tester determines whether a program is correct on
most inputs, and a self-corrector takes a program that is correct on
most inputs and uses it to construct a new program that is correct on
every input with high probability. Program checking is particularly
interesting for problems that are easy to specify but for which
efficient programs may be very complicated. Our goal is to
characterize the functions that have fast and simple checkers. We are
investigating checkers for a variety of problems, including problems
from algebra, graph theory, and computational geometry.
One particularly fruitful line of research concerns self-testers and
self-correctors based on properties satisfied by the function. For
example, the function f(x)=x is uniquely specified by the properties:
(1) for all x,y, f(x)+f(y)=f(x+y)
(2) for all x, f(x)+1=f(x+1)
We have used such properties to construct self-testers and
self-correctors for several classes of functions, including the linear
functions, many of the trigonometric functions, and low degree
polynomial functions. We have recently shown that our results apply to
the setting of real-valued computation, where the output of the
program is approximate instead of exact. Our results borrow techniques
from and have implications for the stability theory of functional
- Office of Naval Research Young Investigator Award (1993-1996)
- 1995 NSF Career Award
- Alfred P. Sloan Research Fellow
- College of Engineering Teaching Award
- On leave 1995-1996 at MIT
- Reviewer: SIAM Journal on Computation; Information and
Computation; IPL; JACM; Algorithmica;
- Member, Program Committee: Symposium on Theory of Computing, May
22-24, 1996, Philadelphia, PA
- Short paths in expander graphs. Daghstuhl Workshop on Online
Algorithms. Dagh-stuhl, Germany, June 23-28 1996.
- On the robustness of functional equations. Dartmouth College,
Hanover, NH, April, 1996.
- ____. DIMACS Workshop on Computational and Complexity Issues in
Automated Verification, Rutgers, NJ, March 25-28, 1996.
- Learning polynomials with queries: The highly noisy case. Workshop on
Randomness Algorithms and Computation, Berkeley, CA, December, 1995.
- ____. 36th IEEE Conference on Foundations of Computer Science,
Milwaukee, WI, November 1995.
- On the robustness of functional equations. Workshop on Checking,
Testing, and Security for Embedded Real-Time Software Systems, Hughes
Aircraft Company, El Segundo, CA, November 10, 1995.
- New directions and applications for learning finite automata. IBM
Yorktown, August 1995.
- ____. Computer Science, University of California, Berkeley, CA, July,
- Designing checkers for programs that run in parallel.
Algorithmica 20, 3 (April 1996), 1-15.
- Robust characterizations of polynomials and their applications to
program testing. SIAM Journal of Computing 25, 2 (April 1996),
252-271 (with M. Sudan).
- Learning polynomials with queries: The highly noisy case.
Proceedings 36th IEEE Conference on Foundations of Computer Science.
October 1995, 294-303 (with O. Goldreich and M. Sudan).
- Efficient algorithms for learning to play repeated games against
computationally bounded adversaries. Proceedings 36th IEEE Conference
on Foundations of Computer Science. October, 1995, 332-341 (with
Y. Freund, M. Kearns, Y. Mansour, D. Ron, and R. Schapire).
- Exactly learning automata with small cover time. Proceedings 8th
Annual ACM Workshop on Computational Learning Theory, 1995. 427-436
(with D. Ron).
- On learning bounded-width branching programs. Proceedings 8th Annual
ACM Workshop on Computational Learning Theory, 1995, 361-368 (with
F. Ergun and S. Ravikumar).
1995-1996 Annual Report Home Page
Departmental Home Page
If you have questions or comments please contact:
Last modified: 2 November 1996 by Denise Moore