Eric Bach


Computer Sciences Department
University of Wisconsin
1210 W. Dayton St.
Madison, WI 53706-1685

telephone: (608) 262-1204
fax: (608) 262-9777
Ph.D., University of California, Berkeley, 1984
Interests: Theoretical computer science, computational number theory, algebraic algorithms, complexity theory, cryptography, six-string automata

Research Summary

I am primarily interested in how one uses computers to efficiently solve algebraic and number-theoretic problems (example: how does one tell if a 100-digit number is prime without examining all possible factors?). These problems have intrinsic mathematical interest, as well as applications to random number generation, codes for reliable and secure information transmission, computer algebra, and other areas. I am presently writing a book on this subject, the first volume of which has just appeared.

I am also interested in applying probability theory to the design and analysis of algorithms. For example, if a large number is composite, it can be proved so by a simple test that uses an auxiliary number, called a `witness.' Finding good estimates for the least witness is a long-standing open problem. Using large deviation theory, I designed accurate heuristic models for least witnesses, primitive roots, and other computationally interesting phenomena. In another application of probability theory, I used martingale theory to analyze the behavior of biochemical methods that may be used someday to solve NP-complete problems.

Sample Recent Publications

Statistical evidence for small generating sets (with L. Huelsbergen), Mathematics of Computation, 1993.

DNA models and algorithms for NP-complete problems (with A. Condon, E. Glaser and S. Tanguay), Proceedings of the 11th Annual Conference on Computational Complexity, 1995.

Algorithmic Number Theory (Volume I: Efficient Algorithms) (with J. Shallit), MIT Press, Cambridge, MA, August 1996.

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