This paper asks when MR-subset selection is a real mutant-level requirement for minimum complete evidence in metamorphic testing rather than a coarse fault-class counting artifact. We define a layer-relative completeness criterion over an admitted mutant--draw coverage universe. The central result is a support-set domination boundary: it states when class-level abstraction is safe and when mutant-level MR minimization is necessary. The boundary is governed by kill-signature heterogeneity, which yields a scoped fault-signature kernel and separates the MR-specific question from ordinary fault-class counting. The resulting Min-MR-Complete problem is Set-Cover-equivalent over the selected coverage universe, giving NP-hardness, the classical logarithmic approximation boundary, a greedy approximation, an exact ILP formulation, and an SMS-rank upper bound that is not a lower bound or tight predictor. Artifact lanes provide lane-local minimization and audit evidence; separately, route witnesses instantiate both collapse and non-collapse regimes for the boundary theorem and are not pooled as population-level experiments. Other MR-class-proxy rows remain intermediate signals rather than route-admitted witness evidence.
翻译:本文探讨了在蜕变测试中,MR子集选择何时是真正面向变异体级别的最小完备证据需求,而非粗糙的故障类别计数产物。我们在一个已接受的变异体-覆盖宇宙上定义了一种层级相对完备性准则。核心结果为支撑集支配边界:它阐明了何时类别级抽象是安全的,以及何时变异体级MR最小化是必要的。该边界由杀伤签名异质性主导,由此产生一个限定范围的故障签名核,并将MR特定问题与普通故障类别计数问题分离。由此衍生的最小完备MR问题在选定覆盖宇宙上等价于集合覆盖问题,从而推导出NP困难性、经典对数近似边界、贪婪近似方法、精确整数线性规划(ILP)公式,以及一个既非下界亦非紧致预测器的SMS秩上界。工件通道提供通道局部最小化与审计证据;路径见证者则分别实例化边界定理的坍缩与非坍缩情形,而非作为总体级实验进行汇总。其他MR类代理行仍为中间信号量,而非路径已接受的见证证据。