sufficient-condition derivation

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.

This work demonstrates a fundamental limitation of unified formal verification methods within the standard Turing model when applied to nontrivial semantic invariants. By formalizing “acceptable verification schemes” as generator–verifier pairs through a model-theoretic lens, the study integrates Rice’s theorem with formal verification frameworks to prove that such schemes implicitly induce undecidable decision procedures. Crucially, this impossibility stems from the computational behavior inherent to the verification mechanism itself, rather than from unprovable complexity-theoretic assumptions. Leveraging computability theory, model theory, and Coq-based formalization, the authors construct an extended structural model capturing semantic–syntactic interactions and rigorously establish that properties related to P vs NP and cryptographic assumptions such as one-way functions cannot be certified by any such unified method. A complete Coq implementation accompanies the theoretical results.

This work addresses the challenge of verifying safety properties for infinite-state parameterized programs under complex topologies by introducing a novel proof system called the “parameterized proof space.” Leveraging local symmetries inherent in program topologies, the approach enables efficient verification of entire families of parameterized programs through the reuse of proof arguments across isomorphic neighborhoods. The key contributions include the development of a relatively complete proof system that operates without requiring explicit axiomatization of the underlying topology, integration of the model-theoretic notion of limit programs to support automatic construction and verification of universally quantified invariants, and the establishment of decidability guarantees for the verification process under certain conditions.

This paper addresses the fundamental question: “How can one design a programming language whose definable functions exactly coincide with all polynomial-time computable problems?” We introduce Polylang—the first imperative language that is both expressively complete for PTIME and equipped with rigorous complexity guarantees. Its core innovation is a static, hierarchy-based resource-sensitive type system that ensures, at compile time, that all well-typed programs terminate within polynomial time. We formally prove that Polylang is Turing-equivalent to PTIME under polynomial-time reductions. We provide a full implementation—including an interpreter and a sound type checker—and validate its expressiveness and analyzability on canonical algorithms (e.g., sorting, bipartite matching, dynamic programming). This work establishes, for the first time in an imperative setting, a precise definability correspondence between a programming language and PTIME, thereby offering a theoretically sound and practically implementable foundation for feasible computation.

Certificates for hyperproperty verification—particularly for HyperLTL-expressible safety and information-flow properties—lack explainability and interactivity. Method: This paper pioneers modeling hyperproperty verification as a quantified game, using existential-player strategies as novel, verifiable, and human-understandable certificates. We develop a game-theoretic semantics for a HyperLTL fragment, enable automated strategy synthesis, and design HyGaViz—a web-based interactive visualization tool that supports user-guided exploration of universal traces to collaboratively validate strategy correctness. Contribution/Results: (1) We establish game strategies as an explainable certificate paradigm for hyperproperty verification; (2) we present the first visualization system supporting strategy-level explanation and human-in-the-loop verification; (3) we empirically validate its conciseness, checkability, and pedagogical utility across multiple information-flow security benchmarks.

This work investigates how to characterize the strength of propositional proof systems via provable reductions to TFNP search problems. To this end, it introduces a novel class of implicit proof systems ⟨EF, R⟩, where R is a TFNP problem such that the task of finding falsifying assignments for unsatisfiable formulas reduces polynomially to R, and the correctness of this reduction is verifiable in Extended Frege (EF). The main contributions include establishing, for the first time, a polynomial equivalence between ⟨EF, Resolution⟩ and the classical sequent calculus G₁; proving that ⟨EF, Iter⟩ is likewise equivalent to both G₁ and ⟨EF, Resolution⟩; and demonstrating that EF-provably correct reductions are strictly stronger than FP-computability. Moreover, for any sufficiently strong proof system P, there exists a search problem Rₚ in FP such that ⟨EF, Rₚ⟩ is polynomially equivalent to P.

研究了非多项式目标和约束的学习问题的最优性和正性证书，通过抽象函数代数上的定理分离目标与约束角色，并构造出证书。

Safety verification of complex systems is often hindered by the difficulty of constructing inductive invariants, intricate Boolean structures, and extensive quantifier alternations. This work proposes an incremental safety proof method that integrates forward reasoning, backward reasoning under time reversal, and a prophecy variable mechanism to decompose global invariants into simpler subgoals. Without expanding the set of candidate invariant formulas, the approach strictly enhances proof power while substantially reducing the logical complexity of required invariants. Experiments on Paxos, its variants, and the Raft protocol demonstrate that the method effectively eliminates complex Boolean structures, reduces quantifier usage and alternation depth, and significantly shrinks the invariant search space.

This work addresses the limitations of traditional patent analysis—namely, the inefficiency of manual approaches and the opacity and non-composability of conventional machine learning methods, which lack formal guarantees. The paper proposes the first hybrid analytical framework integrating artificial intelligence with Lean 4, encoding patent claims as directed acyclic graphs and formalizing intellectual property tasks within dependent type theory to produce machine-checkable certificates verifiable by a trusted kernel. Key innovations include a complete-lattice-based weighted coverage model, a monotonic confidence propagation mechanism, and a fully formally verified core coverage algorithm, exemplified by the coverage = W_cov identity. Empirical evaluation on a synthetic memory module case study demonstrates interpretable weighted coverage analysis and sensitivity verification.

This study addresses the equivalence verification problem between two fundamental representations of finite closure systems—implicational and intersectional canonical bases—specifically, whether an intersectional basis fully captures all closed sets generated by a given set of implications. By integrating techniques from computational complexity theory, formal concept analysis, and functional dependency theory, the work establishes for the first time that this problem is coNP-complete, even when restricted to acyclic implication sets with premises of size at most three. This result precisely characterizes the computational complexity of verifying completeness in closure system representations, rules out the existence of output-polynomial algorithms even in restricted settings such as acyclic convex geometries, and provides new lower bounds for related problems including characteristic model identification.