local-to-global analysis

Existing program logics based on abstract interpretation struggle to systematically handle the principle of locality in heap manipulations and lack a unified approach for deriving local axioms equipped with frame rules. This work proposes a general method that, starting from program semantics and leveraging semantic closure properties, automatically derives separation logic axioms inherently capturing locality and frame rules without syntactic restrictions. The approach enables, for the first time, parameterized and systematic generation of both local axioms and frame rules, uniformly supporting over-approximate and under-approximate reasoning. It is compatible with diverse memory models and logical variants, and establishes a unified framework encompassing both correctness and incorrectness reasoning—successfully demonstrated in the design of novel logics and the derivation of necessary preconditions.

This work establishes lower bounds on certificate size for local certification of distributed graph properties. Focusing on classical properties—including connectivity, matching, and coloring—it introduces the first local hardness reduction framework. By constructing local graph gadgets and applying information-theoretic analysis within the local model, the framework systematically transfers certificate-size lower bounds from one class of properties to another, overcoming the limitations of property-specific proofs. This approach achieves the first transferable lower-bound results in local certification. It uniformly establishes polynomial-scale (Ω(n)) lower bounds for multiple fundamental properties, exposing their inherent local complexity. The framework provides a general tool for local certification theory and advances the understanding of the fundamental limits of distributed verification efficiency.

本文通过构建两个同调理论来解决软件架构中局部与全局语义一致性的问题，并证明了它们的一致性，从而实现了从语义修复到代数几何的转换。

This paper addresses the absence of global variable semantics in region-based functional languages. We propose a unified formalization of type abstraction and region abstraction, naturally deriving the notion of global variables from the Tofte–Talpin region system. By extending the region type system with linear protection mechanisms, we safely model mutable global state—supporting imperative updates while guaranteeing memory safety. Our key contribution is the first demonstration that global variables arise as a logical consequence of unifying region and type abstraction, thereby establishing a deep theoretical connection among region systems, global variables, and linear types. The work includes a formal operational semantics, a sound type system with corresponding typing rules, and a proof of memory safety. It constructs a rigorous theoretical bridge from region-based languages to global state systems, offering a novel paradigm for integrating efficient and safe mutable state into functional languages.

This paper addresses the challenges of fragility analysis and poor constructivity in observational equivalence proofs. We propose a stepwise reasoning method based on hypergraph rewriting. Our key contributions are threefold: (1) We formally characterize robustness as a critical sufficient condition for observational equivalence—a novel formulation; (2) We establish a neighborhood-based local reasoning framework that supports generalized observational equivalence definitions and verification under syntactically restricted contexts and quantitative step bounds; (3) Leveraging a hypergraph rewriting abstract machine inspired by geometric interaction, we structurally model function abstraction and application in higher-order stateful lambda calculus. Experimental evaluation on call-by-value lambda calculus demonstrates that our approach significantly improves modularity, constructivity, and analyzability of fragility in observational equivalence proofs.

This work addresses the inefficiency of traditional finite-domain propagation methods that handle difference constraints $x - y \leq d$ individually. It presents the first global propagator for difference constraints equipped with an explanation mechanism, unifying all such constraints into a single model and enforcing bounds consistency via shortest-path algorithms. The propagator is seamlessly integrated into a lazy clause generation (LCG) solving framework, overcoming the limitations of constraint-by-constraint propagation. For the first time in constraint programming, this approach enables synergistic global reasoning over difference constraints and conflict explanation. Experimental results demonstrate that the proposed method significantly outperforms standard propagation strategies in terms of solving efficiency.

This study addresses privacy leakage in graph data under untrusted environments, as well as the excessive noise and structural loss inherent in existing local differential privacy (LDP) methods. To this end, it proposes a neighborhood-structure-based LDP graph synthesis algorithm. The method estimates triangle counts by aggregating perturbed views and innovatively jointly optimizes degree distribution and triangle statistics objectives to resolve inconsistencies between them, subsequently reconstructing the synthetic graph via a triangle-priority strategy. Experimental results demonstrate that the proposed algorithm significantly outperforms existing baseline methods across multiple graph analysis metrics on four real-world datasets. The source code has been made publicly available.

This work addresses the local certification of $k$-vertex-connectivity and $k$-edge-connectivity in graphs, where short certificates are assigned to vertices so that each node can verify global connectivity using only local neighborhood information. The authors present the first general-purpose local certification scheme applicable to arbitrary $k$, overcoming prior limitations restricted to small values of $k$. By integrating combinatorial tools such as branch decompositions, Eulerian subgraphs, and independent spanning trees, they devise efficient protocols grounded in structural graph properties. For $k \geq 3$, they establish a tight $O_k(\log n)$-bit upper bound for edge-connectivity certification in general graphs, matching the known lower bound; constant-size certificates are achieved for sparse graph classes. Additionally, they prove that certifying 2-vertex-connectivity in general graphs requires certificates of size $\Omega(\log \log^* n)$.

该研究通过消除几何学框架探讨局部最优对象能否由共享部署规则实现，分析信息、架构等因素对缺陷修复的影响。

This study addresses the theoretical drift caused by model modifications and the challenges of automated construction in the formalization of stochastic optimization algorithms. We propose a fully automated formalization framework driven by large language model (LLM) agents. This framework employs proof obligations to guide the automatic construction of Lean models and supporting theories, introduces signature contracts alongside independent auditing mechanisms to prevent assumption weakening, and establishes a reusable verification library, SOptLib, to enable cumulative verification cycles. Experimental results demonstrate that the system achieves an average score of 6.3 out of 7 across 15 tasks, generates 490,000 lines of `sorry`-free code, and identifies 28 formula errors and proof gaps in published literature, thereby realizing highly reliable automated formalization of research-grade algorithms.