arXiv:2603.06710v1 Announce Type: cross Abstract: Mining specifications from execution traces presents an automated way of capturing characteristic system behaviors. However, existing approaches are largely restricted to Boolean abstractions of events, limiting their ability to express data-aware properties. In this paper, we extend mining procedures to operate over richer datatypes. We first establish candidate functions in our domain that cover the set of traces by leveraging Syntax Guided Synthesis (SyGuS) techniques. To capture these function applications temporally, we formalize the semantics of TSL$_f$, a finite-prefix interpretation of Temporal Stream Logic (TSL) that extends LTL$_f$ with support for first-order predicates and functional updates. This allows us to unify a corresponding procedure for learning the data transformations and temporal specifications of a system. We demonstrate our approach synthesizing reactive programs from mined specifications on the OpenAI-Gymnasium ToyText environments, finding that our method is more robust and orders of magnitude more sample-efficient than passive learning baselines on generalized problem instances.

arXiv:2511.02872v4 Announce Type: replace-cross Abstract: Recent advances in large language models (LLMs) have demonstrated impressive capabilities in formal theorem proving, particularly on contest-based mathematical benchmarks like the IMO. However, these contests do not reflect the depth, breadth, and abstraction of modern mathematical research. To bridge this gap, we introduce FATE (Formal Algebra Theorem Evaluation), a new benchmark series in formal algebra designed to chart a course toward advanced mathematical reasoning. We present two new components, FATE-H and FATE-X, each with 100 problems in abstract and commutative algebra. The FATE series spans a difficulty spectrum from undergraduate exercises to problems exceeding PhD qualifying exams. Notably, FATE-X is the first formal benchmark to surpass both PhD-level exam difficulty and the coverage of the Mathlib library. Our evaluations of state-of-the-art LLM provers on this new benchmark reveal a stark performance gap compared to contest math: the best model achieves only 3% (pass@64) accuracy on FATE-H and 0% on FATE-X. Our two-stage evaluation reveals that models' natural-language reasoning is notably more accurate than their ability to formalize this reasoning. We systematically classify the common errors that arise during this formalization process. Furthermore, a comparative study shows that a specialized prover can exhibit less effective reflection than general-purpose models, reducing its accuracy at the natural-language stage. We believe FATE provides a robust and challenging benchmark that establishes essential checkpoints on the path toward research-level formal mathematical reasoning.