Jim Lawrence

IPOG: A General Strategy for T-Way Software Testing

Most existing work on t-way testing has focused on 2-way (or pairwise) testing, which aims to detect faults caused by interactions between any two parameters. However, faults can also be caused by interactions involving more than two parameters. In this paper, we generalize an existing strategy, called in-parameter-order (IPO), from pairwise testing to t-way testing. A major challenge of our generalization effort is dealing with the combinatorial growth in the number of combinations of parameter values. We describe a t-way testing tool, called FireEye, and discuss design decisions that are made to enable an efficient implementation of the generalized IPO strategy. We also report several experiments that are designed to evaluate the effectiveness of FireEye

IPOG-IPOG-D: efficient test generation for multi-way combinatorial testing

Electrical harness manufacturing apparatus comprises wire feeding means for feeding wires along a wire feed path through upstream and downstream (relative to the direction of wire feed) wire guides. The guides have opposed ends which are adjacent to each other during feeding. The guides thereafter move apart so that fed wires are exposed in a gap between the opposed ends. A transferring device clamps the wires in the gap and wire cutting means are provided to cut the wires adjacent to the transferring means, thereby producing leads having their trailing ends gripped in the transferring means. The transferring means transfers the trailing ends laterally of the feed path to a wire connecting station at which the trailing ends are connected to terminals in a connector. Insulation can be stripped, if desired, from the trailing ends of the cut leads and from the leading ends of the wires extending from the feed means.

Refining the in-parameter-order strategy for constructing covering arrays

Covering arrays are structures for well-representing extremely large input spaces and are used to efficiently implement blackbox testing for software and hardware. This paper proposes refinements over the In-Parameter-Order strategy (for arbitrary t). When constructing homogeneous-alphabet covering arrays, these refinements reduce runtime in nearly all cases by a factor of more than 5 and in some cases by factors as large as 280. This trend is increasing with the number of columns in the covering array. Moreover, the resulting covering arrays are about 5 % smaller. Consequently, this new algorithm has constructed many covering arrays that are the smallest in the literature. A heuristic variant of the algorithm sometimes produces comparably sized covering arrays while running significantly faster.

A combinatorial approach to building navigation graphs for dynamic web applications

Modeling the navigation structure of a dynamic web application is a challenging task because of the presence of dynamic pages. In particular, there are two problems to be dealt with: (1) the page explosion problem, i.e., the number of dynamic pages may be huge or even infinite; and (2) the request generation problem, i.e., many dynamic pages may not be reached unless appropriate user requests are supplied. As a user request typically consists of multiple parameter values, the request generation problem can be further divided into two problems: (1) How to select appropriate values for individual parameters? (2) How to effectively combine individual parameter values to generate requests? This paper presents a combinatorial approach to building a navigation graph. The novelty of our approach is two-fold. First, we use an abstraction scheme to control the page explosion problem. In this scheme, pages that are likely to have the same navigation behavior are grouped together, and are represented as a single node in a navigation graph. Grouping pages reduces and bounds the size of a navigation graph for practical applications. Second, assuming that values of individual parameters are supplied by using other techniques or generated manually by the user, we combine parameter values in a way that achieves a well-defined combinatorial coverage called pairwise coverage. Using pairwise coverage can significantly reduce the number of requests that have to be submitted while still achieving effective coverage of the navigation structure. We report a prototype tool called Tansuo, and apply the tool to five open source web applications. Our empirical results indicate that Tansuo can efficiently generate web navigation graphs for these applications.

Trapezoidal and triangular distributions for Type B evaluation of standard uncertainty

The Guide to the Expression of Uncertainty in Measurement (GUM), published by the International Organization for Standardization (ISO), recognizes Type B state-of-knowledge probability distributions specified by scientific judgment as valid means to quantify uncertainty. The ISO-GUM discusses symmetric probability distributions only. Sometimes an asymmetric distribution is needed. We describe a trapezoidal distribution which may be asymmetric depending on the settings of its parameters. We describe the probability density function, cumulative distribution function (cdf), inverse function of the cdf, moment generating function, moments about origin (zero), expected value and variance of a trapezoidal distribution. We show that triangular and rectangular distributions are special cases of the trapezoidal distribution. Then we derive the moment generating functions, moments, expected values and variances of various special cases of the trapezoidal distribution. Finally, we illustrate through a real life example how a Type B asymmetric trapezoidal distribution may be useful in quantifying a correction for bias (systematic error) in a result of measurement and in quantifying the standard uncertainty associated with the correction.

Combinatorial Methods for Event Sequence Testing

Many software testing problems involve sequences of events. This paper applies combinatorial methods to testing problems that have n distinct events, where each event occurs exactly once. The methods described in this paper were motivated by testing needs for systems that may accept multiple communication or sensor connections and generate output to several communication links and other interfaces, where it is important to test the order in which connections occur. Although pair wise event order testing (both A followed by B and B followed by A) has been described, our algorithm ensures that any t events will be tested in every possible t-way order.

Block‐vertex duality and the one‐median problem

The w-centroid problem, denoted by (C), is an optimization problem which has been shown by Kariv and Hakimi to be equivalent, on a tree graph, to the 1-median location problem, denoted by (M). For a general (weighted) connected graph G we develop a duality between (C) (which is defined on G) and a block optimization problem, denoted by (B), and defined over the blocks of G. A block is a maximal nonseparable subgraph. We analyze (B) and (C) by means of two problems equivalent to (B) and (C) respectively, but defined on a blocking graph G which is always a tree. We give an O(∣V∣) algorithm to solve the two problems on G, and we characterize the solutions. We also show that the solution to a 1-median problem defined on G either solves (M) on the original graph G or localizes the search for a solution to (M) to the vertices of a single block. We introduce an extended version of Goldmans algorithm which (in linear time) either solves (M) on G, or finds the single block of G which contains all solutions to (M).

Valuations and polarity

Given a collection of convex polytopes, letτ() denote the set of all convex transversals of. If and ℬ are two such collections, of finite cardinality, then there is a simple, arithmetical condition which holds precisely when τ()=τ(ℬ). Another such condition, involving what we call the “Sallee-Shephard mapping,” characterizes those pairs and ℬ for which τ(τ())=τ(ℬ).As these results are established, several distributive lattices involving convex sets are introduced, and relationships between their valuation modules are determined. In particular, it is proven that the Sallee-Shephard mapping is an isomorphism of the additive, abelian group of simple functions generated by the characteristic functions of the open, convex sets and that generated by those of the closed, convex sets.

Enumeration in torus arrangements

This paper presents two new results of somewhat different flavors. The first result is a formula for the numbers of cells of each dimension determined by an arrangement of closed subgroups of a torus group. This is accompanied by a brief description of previous work on cell counting in torus groups. In the course of things, two distinct formulas yielding the numbers of cells are encountered. The question of how to reconcile these two formulas motivates a general result that applies to lattices whose elements are the closed sets of a closure system. This result gives the characteristic polynomial for the (lattice) dual of such a lattice as a sum of characteristic polynomials of lattices of closed sets of deleted minors of the closure system.

Rectangular distribution whose end points are not exactly known: curvilinear trapezoidal distribution

Metrologists often represent the state of knowledge concerning a quantity about which scant specific information is available by a rectangular probability distribution. The end points are frequently specified by subjective judgment; therefore, they are inexactly known. If the states of knowledge about the end points may be represented by other (narrower) rectangular distributions, then the resulting probability distribution looks like a trapezoid whose sloping sides are curved. We refer to such a probability distribution as curvilinear trapezoid. Depending on the limits of rectangular distributions for the end points, the curvilinear trapezoidal distribution may be asymmetric. In a previous paper we had shown that if the mid-point of a rectangular distribution is known and the state of knowledge about the half-width may be represented by a rectangular distribution then the resulting distribution is symmetric curvilinear trapezoid. In this paper, we describe the probability density function of a curvilinear trapezoidal distribution which arises from inexactly known end points. Then we give compact analytic expressions for all moments including the expected value and the variance. Next we discuss how random numbers from such a distribution may be generated. We compare the curvilinear trapezoid which arises from inexactly known end points with the corresponding trapezoid whose sloping sides are straight. We also compare the curvilinear trapezoid which arises from inexactly known end points with the curvilinear trapezoid which arises when the mid-point is known and the state of knowledge about the half-width may be represented by a rectangular distribution. The results presented in this paper are useful in evaluating uncertainty according to the Guide to the Expression of Uncertainty in Measurement (GUM) as well as Supplement 1 to the GUM (GUM-S1).