A Scalable t-Wise Coverage Estimator: Algorithms and Applications
Why this work is in the frame
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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 <inline-formula><tex-math notation="LaTeX">$t$</tex-math></inline-formula>-wise coverage for higher values of <inline-formula><tex-math notation="LaTeX">$t$</tex-math></inline-formula>. Therefore, designing scalable techniques that can estimate <inline-formula><tex-math notation="LaTeX">$t$</tex-math></inline-formula>-wise coverage for a given set of tests and/or the estimation of maximum achievable <inline-formula><tex-math notation="LaTeX">$t$</tex-math></inline-formula>-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) <inline-formula><tex-math notation="LaTeX">$t$</tex-math></inline-formula>-wise coverage for a given set of tests, and (ii) maximum <inline-formula><tex-math notation="LaTeX">$t$</tex-math></inline-formula>-wise coverage for a given set of constraints. In particular, <inline-formula><tex-math notation="LaTeX">$\mathsf{ApproxCov}$</tex-math></inline-formula> takes in a test set <inline-formula><tex-math notation="LaTeX">$\mathcal{U}$</tex-math></inline-formula> and returns an estimate of the <inline-formula><tex-math notation="LaTeX">$t$</tex-math></inline-formula>-wise coverage of <inline-formula><tex-math notation="LaTeX">$\mathcal{U}$</tex-math></inline-formula> that is guaranteed to be within <inline-formula><tex-math notation="LaTeX">$(1\pm\varepsilon)$</tex-math></inline-formula>-factor of the ground truth with probability at least <inline-formula><tex-math notation="LaTeX">$1-\delta$</tex-math></inline-formula> for a given tolerance parameter <inline-formula><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula> and a confidence parameter <inline-formula><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula>. A scalable framework <inline-formula><tex-math notation="LaTeX">${\mathsf{ApproxMaxCov}}$</tex-math></inline-formula> for a given formula <inline-formula><tex-math notation="LaTeX">${\mathsf{F}}$</tex-math></inline-formula> outputs an approximation which is guaranteed to be within <inline-formula><tex-math notation="LaTeX">$(1\pm\varepsilon)$</tex-math></inline-formula> factor of the maximum achievable <inline-formula><tex-math notation="LaTeX">$t$</tex-math></inline-formula>-wise coverage under <inline-formula><tex-math notation="LaTeX">${\mathsf{F}}$</tex-math></inline-formula>, with probability <inline-formula><tex-math notation="LaTeX">$\geq 1-\delta$</tex-math></inline-formula> for a given tolerance parameter <inline-formula><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula> and a confidence parameter <inline-formula><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula>. Our comprehensive evaluation demonstrates that <inline-formula><tex-math notation="LaTeX">$\mathsf{ApproxCov}$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">${\mathsf{ApproxMaxCov}}$</tex-math></inline-formula> can handle benchmarks that are beyond the reach of current state-of-the-art approaches. In this paper we present proofs of correctness of <inline-formula><tex-math notation="LaTeX">$\mathsf{ApproxCov}$</tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">${\mathsf{ApproxMaxCov}}$</tex-math></inline-formula>, 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 <inline-formula><tex-math notation="LaTeX">$t$</tex-math></inline-formula>.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it