Ronitt Rubinfeld
Assistant Professor
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 equations.


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