Formalizing Regression Testing for Agile and Continuous Integration Environments (2511.02810v1)

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.