Minimum Complete MR Subsets under Semantic-Mutation Fault Models: A Support-Set Domination Boundary

2026-06-06

AI Summary

This study investigates when mutation testing requires selecting a subset of metamorphic relations (MRs) based on concrete mutants—rather than merely counting fault classes—to satisfy minimal completeness evidence requirements. To this end, the authors propose a “layer-wise relative completeness” criterion and introduce a dominance boundary theory driven by heterogeneity in killing signatures, thereby decoupling MR-specific concerns from conventional fault-class statistics. They define a scope-based fault signature kernel and, leveraging a set cover formulation, greedy approximation, integer linear programming, and SMS rank analysis—augmented with artifact channels and path-witness mechanisms—prove that the Min-MR-Complete problem is NP-hard, establish a logarithmic approximation bound, and provide both exact and approximate solution methods. Path witnesses further validate the efficacy of the boundary theorem under both collapsed and non-collapsed scenarios.

Abstract

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.

Problem

• metamorphic testing
• MR-subset selection
• semantic-mutation fault models
• mutant-level completeness
• fault-class counting

Innovation

• support-set domination boundary
• kill-signature heterogeneity
• Min-MR-Complete
• metamorphic testing
• Set-Cover-equivalent