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Context. Several Research areas emerged and have been proceeding independently when in fact they have much in common. These include: mutant subsumption and mutant set minimization; relative correctness and the semantic definition of faults; differentiator sets and their application to test diversity; generate-and--validate methods of program repair; test suite coverage metrics. Objective. Highlight their analogies, commonalities and overlaps; explore their potential for synergy and shared research goals; unify several disparate concepts around a minimal set of artifacts. Method. Introduce and analyze a minimal set of concepts that enable us to model these disparate research efforts, and explore how these models may enable us to share insights between different research directions, and advance their respective goals. Results. Capturing absolute (total and partial) correctness and relative (total and partial) correctness with a single concept: Detector sets. Using the same concept to quantify the effectiveness of test suites, and prove that the proposed measure satisfies appealing monotonicity properties. Using the measure of test suite effectiveness to model mutant set minimization as an optimization problem, characterized by an objective function and a constraint. Generalizing the concept of mutant subsumption using the concept of differentiator sets. Identifying analogies between detector sets and differentiator sets, and inferring relationships between subsumption and relative correctness. Conclusion. This paper does not aim to answer any pressing research question as much as it aims to raise research questions that use the insights gained from one research venue to gain a fresh perspective on a related research issue. mutant subsumption; mutant set minimization; relative correctness; absolute correctness; total correctness; partial correctness; program fault; program repair; differentiator set; detector set. 

To reduce the cost of mutation testing, researchers have sought to find minimal mutant sets. As an optimization problem, mutant set minimization is defined by two parameters: the objective function that we must optimize; and the constraint under which the optimization is carried out. Whereas the objective function of this optimization problem is clear (minimizing the cardinality of the mutant set), the constraint under which this optimization is attempted has not been clearly articulated in the literature. In this paper, we propose a formal definition of this constraint and discuss in what sense, and to what extent, published algorithms of mutant set minimization comply with this constraint.