Kuhn, followed by Tsuchiya and Kikuno, have developed a hierarchy of relationships among several common types of faults (such as variable and expression faults) for specification-based testing by studying the corresponding fault detection conditions. Their analytical results can help explain the relative effectiveness of various fault-based testing techniques previously proposed in the literature. This article extends and complements their studies by analyzing the relationships between variable and literal faults, and among literal, operator, term, and expression faults. Our analysis is more comprehensive and produces a richer set of findings that interpret previous empirical results, can be applied to the design and evaluation of test methods, and inform the way that test cases should be prioritized for earlier detection of faults. Although this work originated from the detection of faults related to specifications, our results are equally applicable to program-based predicate testing that involves logic expressions.

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In this paper we study the MUMCUT strategy that integrates the MUTP, MNFP and CUTPNFP strategies previously proposed separately for testing Boolean specijications. The MUMCUT strategy guarantees to detect seven types of faults found in Boolean expressions. We describe an implementation of generating test sets that satisfy the MUMCUT strategy, and empirically evaluate its cost-effectiveness.With respect to a previously published set of Boolean expressions derived from a real specification, we find that on average the MUMCUT strategy requires only about one quarter of the size of an exhaustive test set. Moreover; the MUMCUT strategy proves to be a substantial improvement to the MAX-A and MAX-B strategies which detect the same types of faults.