Regression Test Window in CI Pipelines

• Regression test window is a defined time interval between builds that limits test execution based on available resources and time constraints in agile and CI environments.
• It employs a build-chain formalism and cost-based scheduling to prioritize and select tests, ensuring maximum fault detection within a constrained time window.
• The framework unifies classical 'retest-all' methods with modern, budget-aware strategies, offering reproducible benchmarking and significant efficiency gains.

A regression test window is a formally defined construct that captures the temporal and methodological constraints faced when performing regression testing between two software builds, particularly within agile and continuous integration (CI) pipelines. In this context, the regression test window models the finite and often strict time budget available to execute a maximally effective subset of regression tests, thereby enabling fine-grained and theoretically grounded trade-offs between test coverage and resource limitations. The regression test window concept unifies and generalizes both classical "retest-all" and modern, budget-constrained regression testing strategies across different domains, including code-based and GUI-based systems.

1. Formal Definitions of Regression Test Window

A regression test window is most precisely characterized using the build-chain formalism for agile and continuous integration environments (Das et al., 4 Nov 2025). Consider two builds in a time-ordered chain:

• $B_i = (P_i, S_i, T_i)$, $B_j = (P_j, S_j, T_j)$, where $P$ is the program version, $S$ the requirements/specifications, and $T$ the set of test cases.
• Let $t_i$ and $t_j$ denote the ready-for-test and deadline times, respectively.

The regression test window is the real interval: $$W_{i,j} = [\,t_i,\;t_{j}\,],\qquad A_{i,j} = t_j - t_i \in \mathbb{R}_{\ge 0}$$ Each test case $t_m \in T_i \cap T_j$ has a setup and execution duration ($t_m^{\mathit{setup}}, t_m^{\mathit{exec}}$), and cost: $$c(t_m) = t_m^{\mathit{setup}} + t_m^{\mathit{exec}}$$ The scope of tests executable within $W_{i,j}$ is given by the monotone function: $$f_W(A_{i,j}) = \max\left\{\,|U|\,\Big|\,U \subseteq T_i\cap T_j,\,\sum_{t_m\in U} c(t_m) \le A_{i,j}\,\right\}$$ where $f_W(A_{i,j})$ is the maximal number of overlapping candidate tests whose total cost does not exceed the window length. If the window is sufficiently large, all candidate tests run, recovering the classical "retest-all"; for finite windows, only a subset can be selected and/or prioritized.

In GUI-based regression testing (Kraus, 2018), a regression test window refers to a captured state/action tuple: $W_i = (s_i,\; \tau_i)$ where $s_i$ is a GUI "WindowDescriptor" snapshot and $\tau_i = (a_{i,1}, ..., a_{i,m})$ is the action sequence to reach $s_i$ from the initial state. This pair is used as an oracle to compare future executions for regression testing.

2. Regression Test Window in Build-Chain Models

The regression test window formalism is embedded within a build-chain abstraction relevant for modern CI pipelines (Das et al., 4 Nov 2025). The pipeline is structured as: $B_1 < B_2 < \cdots < B_n$ with each build tuple $B_i = (P_i, S_i, T_i)$. Regression testing is invoked at each transition $B_i \to B_{i+1}$, with the window $W_{i, i+1} = [t_i, t_{i+1}]$ determining the available time budget $A_i = t_{i+1} - t_i$.

This model provides a unified abstraction for test selection (RTS), minimization (RTM), and prioritization (RTP), with regression test window length directly constraining which and how many tests may be executed.

3. Time Constraints and Scheduling within the Regression Test Window

The regression test window explicitly represents the limited time or resource budget imposed by iterative development cycles (Das et al., 4 Nov 2025, Gu et al., 2024). For each build-to-build transition, let $\mathcal{C} = T_i \cap T_{i+1}$. The subset of executable tests is: $$f_W(A_i) = \max\left\{\,|U|\,\Big|\,U \subseteq \mathcal{C},\,\sum_{t \in U} c(t) \leq A_i\,\right\}$$ A plausible implication is that this formalism enables predictive analysis; for example, shrinking or growing the window allows precise trade-off predictions:

• How many fewer tests execute if the time budget shrinks by 50%?
• What APFD (Average Percentage of Faults Detected) or coverage gain is enabled by increasing $A_i$?

If a utility (quality) function $$Q : \mathsf{Perm}(\mathcal{C}) \rightarrow \mathbb{R}$$ is provided, the regression test window enables prioritization: maximizing expected benefit under fixed budget.

4. Degeneration and Generalization: From Classical to Modern Regression Testing

The regression test window framework subsumes the classical "retest-all" method (Das et al., 4 Nov 2025). In the case where only two builds exist and the window length $A_i \to \infty$, all tests in $T_i \cap T_{i+1}$ can be executed: $f_W(\infty) = |T_i \cap T_{i+1}|$ This recovers standard semantics: $$\mathit{RegAll}(B_i,B_{i+1}) = \begin{cases} 1, & \text{if } \forall t\in T_i\cap T_{i+1}: B_i(t) = B_{i+1}(t) \ 0, & \text{otherwise} \end{cases}$$ The regression test window thereby provides a continuum from budget-limited modern approaches to unrestricted classical regression testing.

In GUI contexts, the "window" as a pair (state, action-sequence) offers a regression-test oracle that sidesteps the need for hand-written assertions, supporting difference testing even when classical oracles are unavailable (Kraus, 2018).

5. Practical Implementations and Algorithms

CI pipelines instantiate the regression test window via systematized build-logging and modular regression test strategies (Das et al., 4 Nov 2025):

• Unified abstraction: Log build tuples $(P_i, S_i, T_i, A_i, Q)$, enabling algorithm-independent comparison and module exchange.
• Budget-aware scheduling: Explicit constraint via $f_W$ enables tools to optimize for maximum defect detection or coverage within a specified window.
• Algorithm substitution: Any RTS, RTM, or RTP algorithm can be plugged in provided it consumes build tuples with window constraints.
• Empirical calibration: Measuring $A_i, c(t), Q$ across builds supports informed cost–benefit decision-making and fine-tuning time boxes.

In assertion-based fine-grained RTS (Gu et al., 2024), the regression test window can be combined with prioritization over assertion-slices. Given assertions $A = \{ a_1, ..., a_{|A|} \}$, and their cost estimates, a prioritization score

$$w(a) = \frac{| \mathit{dep}(a) \cap \Delta_C |}{\mathit{cost}(a)}$$

is used to select and order the assertion executions so as not to exceed the time budget $W$.

In GUI regression, the window object explicitly pairs each observed state with the requisite action trace; monkey testing and ML-based prioritization (using an ANN that achieves 82% accuracy, cf. (Kraus, 2018)) can further focus resources on execution sequences with high defect-revealing potential.

6. Impact, Empirical Results, and Research Comparability

The regression test window abstraction has demonstrable impact on the efficiency, reliability, and reproducibility of regression testing workflows:

• In assertion-based fine-grained RTS, the tool Selertion achieves an average 63% reduction in test time and executes only 15% of assertions, always preserving 100% recall with respect to truly affected assertions (Gu et al., 2024).
• In GUI settings, formalized regression test windows allow ReTest to perform effective difference testing, achieving functionally relevant coverage (pre-ML: 47.82%, post-ML: 46.85%) while generating shorter, more interpretable regression suites (Kraus, 2018).
• The regression test window enables direct comparison of disparate algorithms (e.g., dependency-based, coverage-guided, ML-augmented) under identical constraints, fostering reproducible benchmarking (Das et al., 4 Nov 2025).

Empirical calibration using real cost/benefit data further allows teams to balance time budgets against desired coverage or early-fault detection ROI.

7. Open Challenges and Future Directions

Several open problems and research opportunities stem from operationalizing the regression test window:

• Handling cross-slice interactions and shared state in assertion-based RTS to ensure soundness under side-effectful or stateful tests (Gu et al., 2024).
• Generalizing slicing and dependency analysis to integration, system, and UI tests where the invocation structure is dynamic or opaque.
• Developing and validating learned cost–benefit models for more accurate prioritization within strictly bounded windows.
• Extending the window formalism for multi-threaded, distributed, or real-time systems where test costs and coverage evolve dynamically.

A plausible implication is that as the regression test window formalism is integrated into more toolchains and test orchestrators, empirical evidence on its generality and utility will drive further refinements, leading towards a unified, sound, and comprehensive theory of budget-constrained regression testing.

---

The regression test window formalism establishes a mathematically rigorous and practically actionable foundation for regression testing under temporal and budget constraints. It subsumes both classical and contemporary methodologies, providing a common language and analytical basis across code-based and GUI-based domains, with significant consequences for tool design, empirical evaluation, and the future of regression testing research (Das et al., 4 Nov 2025, Kraus, 2018, Gu et al., 2024).