formal verification

This work addresses the scalability and practicality challenges in modeling operational semantics for programming languages. Methodologically, it introduces a mathematically lightweight yet semantically precise and extensible operational semantics framework, formalizing program computation steps to uniformly support semantic equivalence, reduction semantics, static analysis, compiler correctness proofs, and program property verification. Its key contributions are: (i) systematic modeling of multi-paradigm language features using minimal, accessible mathematical machinery—balancing theoretical rigor with engineering utility; and (ii) significantly enhanced portability and reusability of semantic models, demonstrated through successful formal verification of multiple production compilers and static analyzers. The framework provides a unified, scalable semantic foundation for programming language design, specification standardization, and trustworthy software construction.

Informal natural language requirements in safety-critical systems impede direct application to formal verification. Method: This paper proposes a semi-automated specification generation approach integrating large language models (LLMs) with domain ontologies, comprising ontology-driven semantic parsing of requirements, LLM-guided instantiation of formal specification templates, and structured reuse of existing specification assets—thereby enhancing verifiability and domain consistency. Contribution/Results: We establish a challenge analysis framework addressing requirement ambiguity, logical incompleteness, and formal mapping deviation. Preliminary validation in aviation and rail transit domains demonstrates a 32% improvement in specification generation accuracy and a 45% reduction in manual correction effort. The work provides a scalable, empirically grounded methodology for trustworthy natural-language-to-formal-specification translation.

This paper addresses the lack of a unified formal framework for modeling operational semantics of programming languages and verifying program correctness. We propose a novel unifying framework based on multi-sorted hybrid modal logic—the first application of such a logic to operational semantics modeling—significantly reducing representational distance in semantic encoding. Compared with dynamic logic, our approach more naturally captures program execution dynamics; relative to traditional weakest precondition calculi, it offers superior expressiveness and semantic clarity. The framework uniformly supports semantic definition, property specification, and formal verification. Crucially, we establish key completeness results, thereby laying a theoretically rigorous foundation that retains practical expressivity for formal program verification.

This paper addresses hyperproperties—higher-order system requirements encompassing information-flow security, knowledge reasoning, and robustness, which span multiple execution traces—by proposing the first unified logical and algorithmic framework covering the entire verification lifecycle. Methodologically, it rigorously characterizes the expressive power and decidability boundaries of classical temporal logics (LTL, CTL, S1S) over hyperproperties; then introduces a novel multi-trace synchronization modeling and quantifier alternation handling mechanism grounded in higher-order temporal logic, constraint solving, and symbolic automata. Key contributions include: (i) a comprehensive taxonomy and complexity-theoretic characterization of hyperproperty logics; (ii) an open-source verification toolchain supporting HyperLTL and HyperCTL*; and (iii) end-to-end support for core verification tasks—including satisfiability checking, model checking, runtime monitoring, and controller synthesis.

Automated verification in separation logic (SL) has long relied on ad hoc heuristics, lacking a systematic metatheory and suffering from poor scalability. Method: This paper establishes the first general SL metatheory grounded in category theory and algebraic structures—specifically functors, homomorphisms, and modules over rings—systematically integrating abstract algebra into SL automation. The framework supports compositional model instantiation and modular predicate synthesis for any data structure admitting an algebraic characterization. All results are formally verified in Isabelle/HOL, and an automatic algebraic instantiation algorithm is developed. Contribution/Results: Experiments demonstrate fully automated algebraic modeling of complex imperative program semantics—including lists, trees, and graphs—and yield inference engines whose performance matches state-of-the-art hand-crafted systems. This approach decisively overcomes the scalability limitations inherent in heuristic-based methods.

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 work proposes an end-to-end, large language model (LLM)-driven framework that integrates natural language directly into the formal verification pipeline, addressing the longstanding challenge that existing formal verification methods rely on rigorously defined formal specifications and thus struggle to accommodate safety requirements expressed in natural language. The approach leverages an LLM to automatically translate natural language descriptions into formal safety specifications, which are then used to perform compositional verification of code implementations. By circumventing the traditional dependency on manually crafted formal specifications, the method demonstrates a novel pathway toward bridging informal requirements and rigorous verification. Preliminary experiments indicate its feasibility and potential for enhancing code safety, offering a promising direction for making formal verification more accessible and applicable to real-world software development practices.

This work presents the first successful application of a large language model—specifically, Claude Opus 4.6—as an AI-powered programming assistant to automatically generate and verify a semantic-preserving proof for the Administrative Normal Form (ANF) transformation in the CertiCoq compiler, entirely without manual proof coding. Guided by human oversight and built upon the Rocq proof language, the approach adapts and transfers techniques from an existing continuation-passing style (CPS) transformation proof. Within approximately 96 hours, the system produced 7,800 lines of machine-checkable proof code, surpassing the previous CPS proof of 5,300 lines and substantially reducing development time. This result demonstrates the feasibility and significant potential of large language models in formal verification.

This work addresses inconsistencies arising from structural mismatches between natural language and formal languages during requirements formalization. It proposes a “consistency through formalization” principle, mandating strict logical alignment among natural language, the structured language FRETish, and the formal temporal logic MTL. Guided by this principle, the authors refine the FRETish-to-MTL translation pipeline in NASA’s FRET tool. Their approach uniquely integrates cross-layer consistency constraints into a collaborative framework combining large language models and formal verification tools. This integration not only uncovers and corrects multiple inconsistencies in the original translation but also demonstrates superior correctness and reliability, as substantiated by formal equivalence proofs and empirical evaluation.

This work unifies the modeling of inference rules and proof structures of formal systems within a categorical framework. It introduces a met-variable context representation based on Cartesian PROPs, encodes assumptions and conclusions using spans, and constructs a symmetric monoidal category of proofs with met-variable substitution as the sole primitive operation. This approach is the first to uniformly embed both inference rules and proof structures into the semantics of symmetric monoidal categories, thereby supporting compositional and reusable handling of hypotheses. The authors implement an open-source verification algorithm and surface syntax, successfully encoding formulas, axioms, and representative derivations of first-order logic, and release a functional proof checker.