analyze parametric families

Program analyses often lack robustness in the face of code changes. This work introduces, for the first time, a unified framework grounded in category theory that formalizes programs and their properties as categorical objects, capturing various forms of robustness—such as variable renaming and semantic refinement—via structure-preserving functors. Two implementation pathways are proposed: one lifts constructions from restricted computational models to general-purpose programs, while the other ensures stability in the composition of robust operators within algebraic program analyses. The framework not only uncovers common principles underlying loop summarization and termination analysis but also provides a theoretical foundation and predictability guarantees for developing program analyses that are more resilient to program transformations.

This work addresses the challenge of certifying performance attributes that emerge as user concerns after deployment but were not considered during the design phase in data-driven control. To this end, the paper proposes a two-layer adaptability framework that extends the scenario approach by introducing a post-design adaptability concept, enabling reliable certification without requiring additional test data. It is the first to formally incorporate user-specified a posteriori performance properties into the scenario optimization framework, deriving computable, distribution-free upper and lower bounds on the violation risk. Moreover, the method allows full reconstruction of the performance metric’s distribution from existing data. Experimental validation on H₂ control and pole placement problems demonstrates that the approach effectively certifies a posteriori properties and accurately infers critical performance distributions, offering both theoretical rigor and practical utility.

This study addresses the challenge in software maintenance of effectively quantifying the execution status of internal modules to identify redundant or critical components requiring modification or removal. To this end, it introduces spatial statistics theory into software engineering for the first time, proposing the concept of “software space.” By modeling execution data through a module call graph, the approach enables structured analysis of module-level execution behavior via spatial clustering visualization and statistical hypothesis testing. Experimental results demonstrate that the method successfully identifies both critical and redundant modules, thereby offering data-driven support for informed maintenance decisions.

Manual tuning of abstraction strategies in static program analysis is labor-intensive and struggles to balance precision and efficiency. Method: This paper proposes a fully automated, adaptive abstraction-parameter tuning method for the Frama-C/Eva analyzer. It innovatively models abstraction parameters as probability distributions over lattices and employs an iterative sampling–analysis–Bayesian distribution refinement mechanism to automatically converge on optimal strategy combinations. The method further supports dominant-parameter identification and interpretable analysis. It is implemented as a Frama-C/Eva plugin with an integrated web-based visualization interface. Results: Experiments on multiple complex real-world C programs—including industrial-scale projects—demonstrate significant improvements: average false-positive rate reduction of 32% and average analysis time reduction of 28%. These results validate the method’s effectiveness and state-of-the-art performance in large-scale program analysis.

Automated verification of interactive console I/O programs in Haskell education remains challenging due to the dynamic, history-dependent nature of student implementations. Method: We propose a lightweight, formal behavioral specification language that uniquely integrates global state and execution history, expressed via regex-like syntax; its trace-based semantics enable probabilistic testing and scalable verification through *sampleable validity*. Contribution/Results: Our system automatically validates student submissions against behavioral specifications and supports pedagogical closed-loop applications—including real-time feedback generation, example solution synthesis, and exercise randomization. Empirical evaluation demonstrates substantial improvements in test coverage and pedagogical adaptability while preserving formal rigor. To our knowledge, this is the first framework for verifying interactive behaviors in functional programming education that simultaneously achieves theoretical soundness and practical deployability.

This study addresses the challenge posed by high-dimensional CAD geometric design parameters, which complicate downstream simulation and optimization tasks. While conventional principal component analysis (PCA) struggles to accurately reconstruct the original interpretable parameters from reduced representations, this work systematically examines the impact of each PCA stage on geometric fidelity. It reveals the equivalence between domain-specific PCA variants and standard PCA, and establishes theoretical bounds and conditions under which interpretable parameter reconstruction is feasible. Through geometric parametrization modeling, interpretability analysis, and numerical experiments, the study demonstrates that, under specific conditions, original design parameters can be recovered from PCA representations with high accuracy. These findings provide both theoretical grounding and practical guidance for interpretable dimensionality reduction in high-dimensional geometric design spaces.

Existing statistical model checking methods suffer from insufficient theoretical foundations and limited verification reliability. This work establishes the first comprehensive probabilistic-logical formal framework for the SCAN statistical model checker, integrating probabilistic model checking, statistical hypothesis testing, and formal verification techniques to rigorously characterize the property verification process of complex systems. By unifying these complementary approaches within a sound theoretical basis, the proposed framework not only addresses the foundational gaps previously present in SCAN but also significantly enhances its rigor and applicability. Consequently, it provides a robust guarantee for the reliability of SCAN when applied to the verification of real-world systems.

This study addresses a critical limitation in traditional reproducible research, where sharing only code and results fails to expose the implicit assumptions, expectations, and premises underlying an analyst’s reasoning—thereby hindering thorough evaluation of analytical quality. To overcome this, the paper proposes a formal modeling framework that explicitly translates the analyst’s tacit reasoning process into structured logical representations, statically capturing the construction logic of the analysis. This approach enables systematic scrutiny of the analytical chain of reasoning, assumption sensitivity, and conclusion robustness—even in the absence of the original data. Empirical validation on representative data analysis tasks demonstrates the framework’s effectiveness, achieving both logical visualization and data-free static assessment of analytical integrity.

This work addresses the challenge of irreproducibility in data analysis scripts, which often stems from implicit assumptions—such as specific package versions, expected data formats, or undocumented manual interventions. The paper proposes a static analysis approach tailored to data analysis workflows that, for the first time, unifies diverse implicit assumptions into inferable constraint models. By leveraging customized program analysis and example-driven modeling, the authors develop a prototype system capable of automatically identifying these hidden assumptions, extracting executable preconditions, and generating verifiable constraints. The resulting framework supports runtime validation and automatic documentation generation, substantially enhancing script executability, reproducibility, and interpretability.

This study addresses the significant challenge of verifying termination in real-world C/C++ programs, where loop interactions and nondeterministic inputs complicate analysis. The authors propose a lightweight, tool-agnostic, source-level preprocessing approach that isolates loop obligations via loop slicing and enhances termination analysis by generating input-driven concrete variants tailored to specific scenarios. An empirical evaluation integrating six termination analyzers on 117 real programs demonstrates that slicing conservatively achieves structural isolation, while concretization improves detectability in targeted scenarios at the cost of reduced semantic coverage. Crucially, the combined effect of these techniques is non-additive, indicating that preprocessing should complement—rather than replace—analysis of the original program. The work further reveals substantial variation in how different analyzers respond to preprocessing, offering practical guidance for adaptive usage by developers.