Software and hardware testing using combinatorial covering suites

In the 21^st century our society is becoming more and more dependent on software systems. The safety of these systems and the quality of our lives is increasingly dependent on the quality of such systems. A key element in the manufacture and quality assurance process in software engineering is the testing of software and hardware systems. The construction of efficient combinatorial covering suites has important applications in the testing of hardware and software. In this paper we define the general problem, discuss the lower bounds on the size of covering suites, and give a series of constructions that achieve these bounds asymptotically. These constructions include the use of finite field theory, extremal set theory, group theory, coding theory, combinatorial recursive techniques, and other areas of computer science and mathematics. The study of these combinatorial covering suites is a fascinating example of the interplay between pure mathematics and the applied problems generated by software and hardware engineers. The wide range of mathematical techniques used, and the often unexpected applications of combinatorial covering suites make for a rewarding study.