A program correctness checker is an algorithm for checking the output of a computation. That is, given a program and an instance on which the program is run, the checker certifies whether the output of the program on that instance is correct. This paper defines the concept of a program checker. It designs program checkers for a few specific and carefully chosen problems in the class FP of functions computable in polynomial time. Problems in FP for which checkers are presented in this paper include Sorting, Matrix Rank and GCD. It also applies methods of modern cryptography, especially the idea of a probabilistic interactive proof, to the design of program checkers for group theoretic computations. Two strucural theorems are proven here. One is a characterization of problems that can be checked. The other theorem establishes equivalence classes of problems such that whenever one problem in a class is checkable, all problems in the class are checkable. Supported by NSF Grant #CCR88-136...

Objective measurement of test quality is one of the key issues in software testing. It has been a major research focus for the last two decades. Many test criteria have been proposed and studied for this purpose. Various kinds of rationales have been presented in support of one criterion or another. We survey the research work in

The empirical assessment of test techniques plays an important role in software testing research. One common practice is to instrument faults, either manually or by using mutation operators. The latter allows the systematic, repeatable seeding of large numbers of faults; however, we do not know whether empirical results obtained this way lead to valid, representative conclusions. This paper investigates this important question based on a number of programs with comprehensive pools of test cases and known faults. It is concluded that, based on the data available thus far, the use of mutation operators is yielding trustworthy results (generated mutants are similar to real faults). Mutants appear however to be different from hand-seeded faults that seem to be harder to detect than real faults.

Mutation testing is a technique for unit testing software that, although powerful, is computationally expensive. The principal expense of mutation is that many variants of the test program, called mutants, must be repeatedly executed. This paper quantifies the expense of mutation in terms of the number of mutants that are created, then proposes and evaluates a technique that reduces the number of mutants by an order of magnitude. Selective mutation reduces the cost of mutation testing by reducing the number of mutants. This paper reports experimental results that compare selective mutation testing with standard, or non-selective, mutation testing, and results that quantify the savings achieved by selective mutation testing. The results support the hypothesis that selective mutation is almost as strong as non-selective mutation; in experimental trials selective mutation provides almost the same coverage as non-selective mutation, with a four-fold or more reduction in the number of mutants.

Fault-based testing strategies test software by focusing on specific, common types of faults. The coupling effect hypothesizes that test data sets that detect simple types of faults are sensitive enough to detect more complex types of faults. This paper describes empirical investigations into the coupling effect over a specific class of software faults. All of the results from this investigation support the validity of the coupling effect. The major conclusion from this investigation is the fact that by explicitly testing for simple faults, we are also implicitly testing for more complicated faults, giving us con dence that fault-based testing is an effective way to test software.

Program faults are artifacts that are widely studied, but there are many aspects of faults that we still do not understand. In addition to the simple fact that one important goal during testing is to cause failures and thereby detect faults, a full understanding of the characteristics of faults is crucial to several research areas in testing. These include fault-based testing, testability, mutation testing, and the comparative evaluation of testing strategies. In this workshop paper, we explore the fundamental nature of faults by looking at the differences between a syntactic and semantic characterization of faults. We offer definitions of these characteristics and explore the differentiation. Specifically, we discuss the concept of "size" of program faults -- the measurement of size provides interesting and useful distinctions between the syntactic and semantic characterization of faults. We use the fault size observations to make several predictions about testing and present preliminary data that supports this model. We also use the model to offer explanations about several questions that have intrigued testing researchers.

Constraint-based testing is a novel way of generating test data to detect specific types of common programming faults. The conditions under which faults will be detected are encoded as mathematical systems of constraints in terms of program symbols. A set of tools, collectively called Godzilla, has been implemented that automatically generates constraint systems and solves them to create test cases for use by the Mothra testing system. Experimental results from using Godzilla show that the technique can produce test data that is very close in terms of mutation-adequacy to test data that is produced manually, and at substantially reduced cost. Additionally, these experiments have suggested a new procedure for unit testing, where test cases are viewed as throw-away items rather than scarce resources. 1 INTRODUCTION This paper describes experimental results that are based on a new technique for generating test data. This technique, called constraint-based testing (CBT), uses the source code to automatically generate test data that attempts to satisfy the mutation-adequacy criteria. Elsewhere, we describe the technique [9, 12], and the details and algorithms of the implementation [29]; here we describe a set of experiments that measure CBT.

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Mutation analysis is a powerful technique for assessing and improving the quality of test data used to unit test software. Unfortunately, current automated mutation analysis systems su er from severe performance problems. This paper presents a new method for performing mutation analysis that uses program schemata to encode all mutants for a program into one metaprogram, which is subsequently compiled and run at speeds substantially higher than achieved by previous interpretive systems. Preliminary performance improvements of over 300 % are reported. This method has the additional advantages of being easier to implement than interpretive systems, being simpler to port across a wide range of hardware and software platforms, and using the same compiler and run-time support system that is used during development and/or deployment.

Mutation testing is a technique for testing software units that has great potential for improving the quality of testing, and thereby increasing our ability to assure the high reliability of critical software. It will be shown that recent advances in mutation research have brought a practical mutation testing system closer to reality. One recent advance is a partial solution to the problem of automatically detecting equivalent mutant programs. Equivalent mutants are currently detected by hand, which makes it very expensive and time-consuming. The problem of detecting equivalent mutants is a specific instance of a more general problem, commonly called the feasible path problem, which says that for certain structural testing criteria some of the test requirements are infeasible in the sense that the semantics of the program imply that no test case satis es the test requirements. Equivalent mutants, unreachable statements in path testing techniques, and infeasible DU-pairs in dataflow testing are all instances of the feasible path problem. This paper presents a technique that uses mathematical constraints, originally developed for test data generation, to automatically detect some equivalent mutants and infeasible paths.