A Scalable t-Wise Coverage Estimator: Algorithms and Applications
Bibliographic record
Abstract
Owing to the pervasiveness of software in our modern lives, software systems have evolved to be highly configurable. Combinatorial testing has emerged as a dominant paradigm for testing highly configurable systems. Often constraints are employed to define the environments where a given system is expected to work. Therefore, there has been a sustained interest in designing constraint-based test suite generation techniques. A significant goal of test suite generation techniques is to achieve$t$-wise coverage for higher values of$t$. Therefore, designing scalable techniques that can estimate$t$-wise coverage for a given set of tests and/or the estimation of maximum achievable$t$-wise coverage under a given set of constraints is of crucial importance. The existing estimation techniques face significant scalability hurdles. We designed scalable algorithms with mathematical guarantees to estimate (i)$t$-wise coverage for a given set of tests, and (ii) maximum$t$-wise coverage for a given set of constraints. In particular,$\mathsf{ApproxCov}$takes in a test set$\mathcal{U}$and returns an estimate of the$t$-wise coverage of$\mathcal{U}$that is guaranteed to be within$(1\pm\varepsilon)$-factor of the ground truth with probability at least$1-\delta$for a given tolerance parameter$\varepsilon$and a confidence parameter$\delta$. A scalable framework${\mathsf{ApproxMaxCov}}$for a given formula${\mathsf{F}}$outputs an approximation which is guaranteed to be within$(1\pm\varepsilon)$factor of the maximum achievable$t$-wise coverage under${\mathsf{F}}$, with probability$\geq 1-\delta$for a given tolerance parameter$\varepsilon$and a confidence parameter$\delta$. Our comprehensive evaluation demonstrates that$\mathsf{ApproxCov}$and${\mathsf{ApproxMaxCov}}$can handle benchmarks that are beyond the reach of current state-of-the-art approaches. In this paper we present proofs of correctness of$\mathsf{ApproxCov}$,${\mathsf{ApproxMaxCov}}$, and of their generalizations. We show how the algorithms can improve the scalability of a test suite generator while maintaining its effectiveness. In addition, we compare several test suite generators on different feature combination sizes$t$.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.017 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.006 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".