Toward a Better Understanding of Probabilistic Delta Debugging

2024-08-08

AI Summary

Probabilistic Delta Debugging (ProbDD) exhibits superior empirical performance, yet its theoretical underpinnings and the precise role of randomness remain unclear. Method: We conduct a theoretical deconstruction of ProbDD, revealing that its advantage stems not from randomness per se but from skipping redundant queries. Leveraging this insight, we propose Certainty-based Delta Debugging (CDD), a deterministic, low-complexity algorithm grounded in Bayesian modeling. We validate CDD via ablation studies and comprehensive evaluation across 76 test cases spanning input minimization and software thinning tasks. Contribution/Results: CDD matches ProbDD’s empirical performance exactly while reducing theoretical time complexity significantly. It eliminates stochasticity, yielding a simpler, fully interpretable, and more deployable solution. This work provides the first rigorous mechanistic explanation of ProbDD’s efficacy and establishes a sounder, more efficient theoretical foundation for Delta Debugging—along with a practical, deterministic alternative.

Technology Category

• Reasoning under Uncertainty: Probabilistic Programming
• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Diagnosis and Abductive Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Given a list L of elements and a property that L exhibits, ddmin is a well-known test input minimization algorithm designed to automatically eliminate irrelevant elements from L. This algorithm is extensively adopted in test input minimization and software debloating. Recently, ProbDD, an advanced variant of ddmin, has been proposed and achieved state-of-the-art performance. Employing Bayesian optimization, ProbDD predicts the likelihood of each element in L being essential, and statistically decides which elements and how many should be removed each time. Despite its impressive results, the theoretical probabilistic model of ProbDD is complex, and the specific factors driving its superior performance have not been investigated. In this paper, we conduct the first in-depth theoretical analysis of ProbDD, clarifying trends in probability and subset size changes while simplifying the probability model. Complementing this analysis, we perform empirical experiments, including success rate analysis, ablation studies, and analysis on trade-offs and limitations, to better understand and demystify this state-of-the-art algorithm. Our success rate analysis shows how ProbDD addresses bottlenecks of ddmin by skipping inefficient queries that attempt to delete complements of subsets and previously tried subsets. The ablation study reveals that randomness in ProbDD has no significant impact on efficiency. Based on these findings, we propose CDD, a simplified version of ProbDD, reducing complexity in both theory and implementation. Besides, the performance of CDD validates our key findings. Comprehensive evaluations across 76 benchmarks in test input minimization and software debloating show that CDD can achieve the same performance as ProbDD despite its simplification. These insights provide valuable guidance for future research and applications of test input minimization algorithms.

Problem

• ProbDD algorithm
• probability Delta debugging
• CDD design

Innovation

• CDD algorithm
• ProbDD optimization
• ddmin performance comparison