#
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 at cs dot wisc dot 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.

## Some Recent Papers:

Computing prime harmonic sums
(with J. Sorenson and D. Klyve),
*Mathematics of Computation* 78, 2283-2305, 2009.
Improved asymptotic formulas for counting correlation immune
Boolean functions,
*SIAM Journal on Discrete Mathematics* 23, 1525-1528, 2009.

Iterative root approximation methods in p-adic numerical analysis,
*Journal of Complexity* 25, 511-529, 2009.

A novel information transmission problem and its optimal solution
(with J.-Y. Cai),
*Communications in Information and Systems* 9, 141-162, 2009.

Absorption probabilities for the two-barrier quantum walk
(with L. Borisov), ArXiv quant-ph 0901.4349.

This page last edited March 2011.