Eric Bach

Professor

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

telephone: (608) 262-1204
fax: (608) 262-9777
email: bach@cs.wisc.edu
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 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 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.' In practice one usually finds a witness by direct search among the small primes. This leads to the following natural question. How large is the least witness, as a function of the number tested? In recent work, we have given an accurate heuristic model, based on probabilistic assumptions, that allows this, and similar questions, to be answered.

Recent Publications

Improved approximations for Euler products, Proc. CNTA-4 (Canadian Math. Soc. Proceedings, v. 15) , 1995.

DNA models and algorithms for NP-complete problems (with A. Condon, E. Glaser, S. Tanguay), Proc. 11th Annual Conf. on Computational Complexity, 1996.

Algorithmic Number Theory (Volume I: Efficient Algorithms) (with J. Shallit), MIT Press, 1996. For info click on ANT-1.

Curriculum Vitae


This page created July 30, 1996.
Email bach@cs.wisc.edu to report errors.