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Michal Buran

Publications and source records attributed to Michal Buran.

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HoF-Bench: Rediscovering Real AI-Discovered CVEs Without Frontier Models

LLM-based analyzers have begun finding real vulnerabilities in mature open-source projects: AISLE's analyzer is credited with more than 280 CVEs across 78 projects, including OpenSSL, curl, and GnuTLS. We introduce HoF-Bench (named after AISLE's public Hall of Fame), a benchmark built from 95 of these public AI-discovered CVEs across eight repositories pinned at vulnerable commits. Analyzers receive source and target-file scope but not CVE identifiers, descriptions, fixes, or expected mechanisms; a detector-blinded frontier-model judge credits only findings that identify the same code path, root cause, attack condition, and impact. A deliberately minimal LLM-based analyzer rediscovers up to 65 of the 95 CVEs (68%) under this strict protocol. No frontier model performs detection anywhere in the study. The ten detector backbones are five open-weight models (21B--284B total parameters, 3--13B active) and five proprietary small or "flash"-tier models. All of them run in the fixed scaffold with four repeated passes, an optional generated-context stage, and a replayable multi-round triage stage (7,600 model--CVE pass records). Difficulty is strongly structured by language; the CVEs missed by every model concentrate in C infrastructure code. HoF-Bench provides a compact test bed for comparing vulnerability scanners, their reliability across repeated runs, and the candidate volume they create. The dataset is available at https://huggingface.co/datasets/aisleinc/HoF-Bench.

cs.CR

One or Nothing: Anti-unification over the Simply-Typed Lambda Calculus

Generalization techniques have many applications, including template construction, argument generalization, and indexing. Modern interactive provers can exploit advancement in generalization methods over expressive type theories to further develop proof generalization techniques and other transformations. So far, investigations concerned with anti-unification (AU) over $\lambda$-terms and similar type theories have focused on developing algorithms for well-studied variants. These variants forbid the nesting of generalization variables, restrict the structure of their arguments, and are \textit{unitary}. Extending these methods to more expressive variants is important to applications. We consider the case of nested generalization variables and show that the AU problem is \textit{nullary} (using \textit{capture-avoiding} substitutions), even when the arguments to free variables are severely restricted.

cs.LO

Separability and Randomness in Free Groups

We prove new separability results about free groups. Namely, if $H_1, \ldots , H_k$ are infinite index, finitely generated subgroups of a non-abelian free group $F$, then there exists a homomorphism onto some alternating group $f:F \twoheadrightarrow A_m$ such that whenever $H_i$ is not conjugate into $H_j$, then $f(H_i)$ is not conjugate into $f(H_j)$. The proof is probabilistic. We count the expected number of fixed points of $f(H_i)$'s and their subgroups under a carefully constructed measure.

math.GR

Alternating quotients of right-angled Coxeter groups

Let $W$ be a right-angled Coxeter group corresponding to a finite non-discrete graph $\mathcal{G}$ with at least $3$ vertices. Our main theorem says that $\mathcal{G}^c$ is connected if and only if for any infinite index quasiconvex subgroup $H$ of $W$ and any finite subset $\{ γ_1, \ldots , γ_n \} \subset W \setminus H$ there is a surjection $f$ from $W$ to a finite alternating group such that $f (γ_i) \notin f (H)$. A corollary is that a right-angled Artin group splits as a direct product of cyclic groups and groups with many alternating quotients in the above sense. Similarly, finitely generated subgroups of closed, orientable, hyperbolic surface groups can be separated from finitely many elements in an alternating quotient, answering positively a conjecture of Wilton.

math.GT