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Vasilii Nesterov

Publications and source records attributed to Vasilii Nesterov.

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Agent-Driven Verification of Memory Safety for liblzma Decoder Components with VST

We report on the verification of memory safety for decoder components of liblzma, the compression library underlying xz-utils: the LZMA2 state machine, the LZMA1 decoder it controls, the outer decoding path, and the shared sliding-window dictionary. Built with the Verified Software Toolchain (VST), machine-checked body theorems establish memory safety and partial functional correctness. Across 27 completed body proofs, the largest covers lzma decode, whose 338 source lines expand to 1,934 lines of C after preprocessing; its proof comprises 183,268 lines of proof script over 775,768 lines of mechanically extracted goal statements. The verification exposed undefined behavior in raw LZMA1 zero-input handling, where range-decoder macros add zero to a null pointer and subtract two null pointers. Unlike similar work that synthesizes verified code, we verify pre-existing, production-scale C. AI agents complete proof goals and propose refinements; humans write and review models and specifications, and approve semantic changes; the Rocq kernel checks the proof terms. With agents constructing the proof scripts, the main engineering problems lay in translating and modeling production C, building a robust harness for driving Rocq, and providing feedback for proving agents. VST's assertion logic expressed every contract required by the development. We describe the pipeline, coordination mechanisms, and proof-engineering techniques that resolved these frictions.

cs.SE

FormalProofBench: Can Models Write Graduate Level Math Proofs That Are Formally Verified?

We present FormalProofBench, a private benchmark designed to evaluate whether AI models can produce formally verified mathematical proofs at the graduate level. Each task pairs a natural-language problem with a Lean~4 formal statement, and a model must output a Lean proof accepted by the Lean 4 checker. FormalProofBench targets advanced undergraduate and graduate mathematics, with problems drawn from qualifying exams and standard textbooks across topics including analysis, algebra, probability, and logic. We evaluate a range of frontier models with an agentic harness, and find that the best-performing foundation model achieves 33.5% accuracy, with performance dropping rapidly after that. In addition to the accuracy numbers, we also provide empirical analysis of tool-use, failure modes, cost and latency, thereby providing a thorough evaluation of the formal-theorem proving abilities of frontier models.

cs.AI