An unexpected meeting of four seemingly unrelated problems: graph testing, DNA complex screening, superimposed codes and secure key distribution

This paper discusses the relation among four problems: graph testing, DNA complex screening, superimposed codes and secure key distribution. We prove a surprising equivalence relation among these four problems, and use this equivalence to improve current results on graph testing. In the rest of this paper, we give a lower bound for the minimum number of tests on DNA complex screening model. The first and second author would like to dedicate this paper to professor Frank K. Hwang on the occasion of his 65th birthday. This research is partially supported by Republic of China, National Science Council grant NSC 92-2115-M-009-014.