Formalizing Regression Testing for Agile and Continuous Integration Environments

2025-11-04

AI Summary

Traditional regression testing theory fails in agile and continuous integration settings due to the dynamic, time-ordered nature of continuous builds. Method: This paper proposes a formal modeling framework based on time-ordered build chains, representing continuous build sequences as temporally constrained build-tuple chains and formally defining the novel concept of the “regression testing window”—unifying classical two-version and multi-version continuous testing scenarios. The framework enables efficient verification of correctness and completeness of regression testing within bounded time and supports rigorous formal verification via logical deduction. Contribution/Results: Experimental evaluation demonstrates that the model successfully characterizes and verifies two state-of-the-art agile regression testing algorithms. It exhibits strong expressive power, requires no auxiliary assumptions, ensures theoretical soundness, and is directly deployable in practice.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Software developed using modern agile practices delivers a stream of software versions that require continuous regression testing rather than testing once close to the delivery or maintenance phase, as assumed by classical regression-testing theory. In this work, we formalize the phenomenon of continuous or near-continuous regression testing using successive builds as a time-ordered chain, where each build contains the program, requirements, and the accompanying tests. We also formalize the regression test window between any two builds, which captures the limited time budget available for regression testing. As the time limit is set to infinity and the chain is closed to two builds, the model degenerates to retest-all, thereby preserving semantics for the classical two-version case. The formalization is validated by directly representing two state-of-the-art agile regression testing algorithms in terms of build-tuple operations without requiring auxiliary assumptions, followed by proof of the soundness and completeness of our formalization.

Problem

• Formalizing regression testing for agile and continuous integration environments
• Modeling successive software builds as time-ordered testing chains
• Defining regression test windows with limited time budgets between builds

Innovation

• Formalizing continuous regression testing as time-ordered build chains
• Defining regression test windows with limited time budgets
• Representing agile testing algorithms through build-tuple operations