TCS-BENCH: Benchmarking State-of-the-Art Generative AI Theoretical Computer Science Research Ability

FormalTCS: Benchmarking End-to-End Frontier Formal Theoretical Computer Science Research of Large Language Models

An automated TCS research framework that generates, formalizes, filters, and proves new claims, and further develops an automated TCS research framework that generates, formalizes, filters, and proves new claims.

A light-weight proof checker for TSTP refutations

A proof checker called Nörgler is introduced that builds upon and extends the established approach pioneered by GDV and supports checking propositional, (untyped and typed) first-order, and higher-order refutations represented in TSTP.

Feedback & Synthesis in LLM-Assisted Termination Proofs

Beyond the Answer Key: Robustness Evaluation of Large Language Models for Step-Level Mathematical Verification

Large language models (LLMs) are increasingly used as graders, verifiers, and process auditors, but most mathematical evaluations still emphasize final-answer accuracy. This can obscure whether a model can verify a non-canonical but valid solution trace. We introduce a controlled linear-equation benchmark for evaluating LLMs in the evaluator role. Each instance asks the model to judge final-answer correctness, step-level trace correctness, and the first incorrect step. Our evaluation of state-of-the-art open LLMs reveals a significant robustness gap: models that accurately evaluate canonical solutions often fail when presented with perturbed but logically equivalent variants. Across GPT-OSS 20B, Qwen3-14B, and Phi-4-Reasoning, base models perform well on canonical traces but degrade substantially on perturbed traces, especially for error localization. On valid perturbed traces, base-model false-rejection rates reach 75.6-85.3%, showing strong sensitivity to canonical solution form. Supervised fine-tuning, distillation, and test-time compute improve robustness in some settings, but gains are model dependent and can trade off against canonical performance. The results show that reliable process-level verification remains challenging, and evaluator robustness should be measured separately from solver accuracy, even in a simple algebraic domain with exact ground truth.

PROVE-RT: Generating Mechanized Theorem Prover Scripts for Real-Time Systems using LLMs

Schedulability analysis is essential for certifying real-time systems, but existing tests are often developed through pen-and-paper proofs that are difficult to scale, validate, and maintain. Mechanized verification in PROSA/ROCQ offers a rigorous alternative, yet manually constructing such proofs requires substantial domain expertise and proof-engineering effort. Recent successes of large language models (LLMs) across a wide range of tasks make them promising candidates for generating PROSA/ROCQ scripts for mechanized theorem provers. However, state-of-the-art LLMs often lack the PROSA-specific knowledge required to correctly use its modeling abstractions and proof patterns. This paper introduces PROVE-RT, an LLM-assisted framework for generating PROSA/ROCQ scripts to mechanize schedulability analyses in real-time systems literature. PROVE-RT guides generation through dependency-aware informal sketches, retrieval from processed PROSA documentation, staged skeleton generation, and proof completion. We construct a mechanization-oriented corpus from 1, 191 real-time systems papers, containing 13, 134 informal sketches with dependency information. On a curated evaluation set, direct prompting of state-of-the-art LLMs fails to reliably generate valid PROSA mechanizations, whereas PROVE-RT achieves a success rate of 44.7%. These results show that retrieval-guided and staged LLM assistance can improve automated mechanization of schedulability analysis in PROSA/ROCQ.

AdvancedMathBench: A Benchmark Suite for Advanced Mathematical Proof Generation and Verification

Large language models (LLMs) have achieved remarkable performance on high-school and olympiad-style mathematics, yet their capabilities on advanced mathematics remain poorly understood. Existing benchmarks, however, fall short in both scope and evaluation granularity: they provide limited disciplinary coverage and often rely on final-answer correctness or coarse judgments, leaving the validity of the reasoning process inadequately assessed. To bridge this gap, we introduce AdvancedMathBench, a benchmark suite designed to evaluate advanced mathematical reasoning capabilities. Its core proof-generation benchmark, ProverBench, contains 296 problems spanning undergraduate and doctoral qualifying-exam levels. To provide reliable evaluation of the proofs, we develop a dedicated automatic verification pipeline trained on large-scale expert annotations to produce both correctness verdicts and fine-grained assessments of proof errors, which exhibits strong agreement with human experts on held-out proof trajectories. We further introduce VerifierBench, consisting of 888 model-generated proof trajectories paired with expert ground truth, to evaluate whether models can correctly judge proof validity and provide sound verification rationales. Experiments show that AdvancedMathBench remains challenging for frontier models. On proof generation, the best-performing model, GPT-5.5-xhigh, achieves only 75.8 and 66.1 on the UGD and QE splits, respectively, indicating substantial room for improvement on advanced mathematical proof construction. On proof verification, the best model attains a Balanced F1 of only 65.1, and models generally exhibit low true negative rates, suggesting that critical error detection remains a major bottleneck.