There has been a good deal of research on covering arrays over the last 20 years. Most of this work has focused on constructions, applications and generalizations of covering arrays. The main focus of this thesis is a generalization of covering arrays, covering arrays on graphs. The original motivation for this generalization was to improve applications of covering arrays to testing systems and...

Let q be a prime power and Fq be the finite field with q elements. A q-ary m-sequence is a linear recurrence sequence of elements from Fq with the maximum possible period. A covering array CA(N ; t, k, v) of strength t is a N ×k array with entries from an alphabet of size v, with the property that any N×m subarray has at least one row equal to every possible m-tuple of the alphabet. The coverin...

Modern software systems often consist of many different components, each with a number of options. Although unit tests may reveal faulty options for individual components, functionally correct components may interact in unforeseen ways to cause a fault. Covering arrays are used to test for interactions among components systematically. A two-stage framework, providing a number of concrete algori...

Covering array generation (CAG) is the key research problem in combinatorial testing and an NP-complete problem. With increasing complexity of software under test need for higher interaction covering strength t, techniques constructing high-strength arrays are expected. This paper presents a hybrid heuristic memetic algorithm named QSSMA CAG The sub-optimal solution acceptance rate introduced t...

The minimum number of rows in covering arrays (equivalently, surjective codes) and radius-covering arrays (equivalently, surjective codes with a radius) has been determined precisely only in special cases. In this paper, explicit constructions for numerous best known covering arrays (upper bounds) are found by a combination of combinatorial and computational methods. For radius-covering arrays,...

A covering array of size N, degree k, order v and strength t is a k N array with entries from a set of v symbols such that in any t N subarray every t 1 column occurs at least once. Covering arrays have been studied for their applications to drug screening and software testing. We present explicit constructions and give constructive upper bounds for the size of a covering array of strength three.

Two vectors x, y in Zg are qualitatively independent if for all pairs (a, b) ∈ Zg×Zg, there exists i ∈ {1, 2, . . . , n} such that (xi, yi) = (a, b). A covering array on a graph G, denoted by CA(n,G, g), is a |V (G)|×n array on Zg with the property that any two rows which correspond to adjacent vertices in G are qualitatively independent. The number of columns in such array is called its size. ...

A covering array t-CA(n,k,g), of size n, strength t, degree k, and order g, is a k× n array on g symbols such that every t × n sub-array contains every t × 1 column on g symbols at least once. Covering arrays have been studied for their applications to software testing, hardware testing, drug screening, and in areas where interactions of multiple parameters are to be tested. In this paper, we p...

Software test suites based on the concept of interaction testing are very useful for testing software components in an economical way. Test suites of this kind may be created using mathematical objects called covering arrays. A covering array, denoted by CA(N; t, k, v), is an N × k array over [Formula: see text] with the property that every N × t sub-array covers all t-tuples of [Formula: see t...