Avoiding coincidental correctness in boundary value analysis

In partition analysis we divide the input domain to form subdomains on which the system's behaviour should be uniform. Boundary value analysis produces test inputs near each subdomain's boundaries to find failures caused by incorrect implementation of the boundaries. However, boundary value analysis can be adversely affected by coincidental correctness---the system produces the expected output, but for the wrong reason. This article shows how boundary value analysis can be adapted in order to reduce the likelihood of coincidental correctness. The main contribution is to cases of automated test data generation in which we cannot rely on the expertise of a tester

Evaluating testing methods by delivered reliability

There are two main goals in testing software: (1) to achieve adequate quality (debug testing), where the objective is to probe the software for defects so that these can be removed, and (2) to assess existing quality (operational testing), where the objective is to gain confidence that the software is reliable. Debug methods tend to ignore random selection of test data from an operational profile, while for operational methods this selection is all-important. Debug methods are thought to be good at uncovering defects so that these can be repaired, but having done so they do not provide a technically defensible assessment of the reliability that results. On the other hand, operational methods provide accurate assessment, but may not be as useful for achieving reliability. This paper examines the relationship between the two testing goals, using a probabilistic analysis. We define simple models of programs and their testing, and try to answer the question of how to attain program reliability: is it better to test by probing for defects as in debug testing, or to assess reliability directly as in operational testing? Testing methods are compared in a model where program failures are detected and the software changed to eliminate them. The “better” method delivers higher reliability after all test failures have been eliminated. Special cases are exhibited in which each kind of testing is superior. An analysis of the distribution of the delivered reliability indicates that even simple models have unusual statistical properties, suggesting caution in interpreting theoretical comparisons

A trivariate interpolation algorithm using a cube-partition searching procedure

In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported weight functions. The partition of unity algorithm is efficiently implemented and optimized by connecting the method with an effective cube-partition searching procedure. More precisely, we construct a cube structure, which partitions the domain and strictly depends on the size of its subdomains, so that the new searching procedure and, accordingly, the resulting algorithm enable us to efficiently deal with a large number of nodes. Complexity analysis and numerical experiments show high efficiency and accuracy of the proposed interpolation algorithm

Comparing test sets and criteria in the presence of test hypotheses and fault domains

A number of authors have considered the problem of comparing test sets and criteria. Ideally test sets are compared using a preorder with the property that test set T1 is at least as strong as T2 if whenever T2 determines that an implementation p is faulty, T1 will also determine that p is faulty. This notion can be extended to test criteria. However, it has been noted that very few test sets and criteria are comparable under such an ordering; instead orderings are based on weaker properties such as subsumes. This paper explores an alternative approach, in which comparisons are made in the presence of a test hypothesis or fault domain. This approach allows strong statements about fault detecting ability to be made and yet for a number of test sets and criteria to be comparable. It may also drive incremental test generation

Testing a system specified using Statecharts and Z

A hybrid specification language SZ, in which the dynamic behaviour of a system is described using Statecharts and the data and the data transformations are described using Z, has been developed for the specification of embedded systems. This paper describes an approach to testing from a deterministic sequential specification written in SZ. By considering the Z specifications of the operations, the extended finite state machine (EFSM) defined by the Statechart can be rewritten to produce an EFSM that has a number of properties that simplify test generation. Test generation algorithms are introduced and applied to an example. While this paper considers SZ specifications, the approaches described might be applied whenever the specification is an EFSM whose states and transitions are specified using a language similar to Z

Comparing the effectiveness of testing methods in improving programs: the effect of variations in program quality

We compare the efficacy of different testing methods for improving the reliability of software. Specifically, we use modelling to compare “operational” testing, in which test cases are chosen according to their probability of occurring in actual use of the software, against “debug” testing methods, in which the testers look for test cases which they consider likely to cause failure, or that satisfy some coverage criterion. We base our comparisons on the reliability reached by the program at the end of testing. Differently from previous studies, we consider the probability distribution of the achieved reliability, and thus the probability of satisfying specific requirements, rather than just the average reliability achieved. We take account of two sources of variation. The variation between the actual test histories that are possible for a given program and a given test method: and the fact that different programs start testing with different faults and initial reliability levels. By necessity, we use very simplified models of reality. Yet, we can show some interesting conclusions with important practical consequences. In general, there are stronger arguments in favor of operational testing than previous studies have show

Concurrent algorithms for transient nonlinear FE analysis

A two-parameter class of time-stepping algorithms for nonlinear structural dynamics is investigated. What sets the present method apart from other concurrent algorithms is the fact that it can be used to some advantage in sequential machines as well. Thus, substantial speed-ups are obtained on a single processor as the number of subdomains is increased. An additional O(p) speed-up is obtained when p processors are utilized. The test case discussed is being repeated for a mesh comprising four times as many elements, in an effort to understand how the large scale asymptotic speed-ups are attained. A three dimensional example involving finite deformations and free body motions is also being pursued. A code optimized for concurrency in the Alliant FX8 computer is being finalized. This will provide the means for testing the performance of the algorithm in a multiprocessor environment

Expanding an extended finite state machine to aid testability

The problem of testing from an extended finite state machine (EFSM) is complicated by the presence of infeasible paths. This paper considers the problem of expanding an EFSM in order to bypass the infeasible path problem. The approach is developed for the specification language SDL but, in order to aid generality, the rewriting process is broken down into two phases: producing a normal form EFSM (NF-EFSM) from an SDL specification and then expanding this NF-EFSM