When Verification Hurts: Asymmetric Effects of Multi-Agent Feedback in Logic Proof Tutoring

Large language models (LLMs) are increasingly used for automated tutoring, but their reliability in structured symbolic domains remains unclear. We study step-level feedback for propositional logic proofs, which require precise symbolic reasoning aligned with a learner's current proof state. We introduce a knowledge-graph-grounded benchmark of 516 unique proof states with step-level annotations and difficulty metrics. Unlike prior tutoring evaluations that rely on model self-assessment or binary correctness, our framework enables fine-grained analysis of feedback quality against verified solution paths. We evaluate three role-specialized pipelines with varying solution access: Tutor (partial solution access), Teacher (full derivation access), and Judge (verification of Tutor feedback). Our results reveal a striking asymmetry: verification improves outcomes when upstream feedback is error-prone (<70% accuracy), but degrades performance by 4-6 percentage points through over-specification when feedback is already reliable (>85%). Critically, we identify a shared complexity ceiling; no model or pipeline reliably succeeds on proof states exceeding complexity 4-5. These findings challenge the assumption that adding verifiers or richer context universally improves tutoring, motivating adaptive, difficulty-aware architectures that route problems by estimated complexity and upstream reliability.

Enhancing Mathematical Problem Solving in LLMs through Execution-Driven Reasoning Augmentation

Mathematical problem solving is a fundamental benchmark for assessing the reasoning capabilities of artificial intelligence and a gateway to applications in education, science, and engineering where reliable symbolic reasoning is essential. Although recent advances in multi-agent LLM-based systems have enhanced their mathematical reasoning capabilities, they still lack a reliably revisable representation of the reasoning process. Existing agents either operate in rigid sequential pipelines that cannot correct earlier steps or rely on heuristic self-evaluation that can fail to identify and fix errors. In addition, programmatic context can distract language models and degrade accuracy. To address these gaps, we introduce Iteratively Improved Program Construction (IIPC), a reasoning method that iteratively refines programmatic reasoning chains and combines execution feedback with the native Chain-of-thought abilities of the base LLM to maintain high-level contextual focus. IIPC surpasses competing approaches in the majority of reasoning benchmarks on multiple base LLMs. All code and implementations are released as open source.

LLMs' Reshaping of People, Processes, Products, and Society in Software Development: A Comprehensive Exploration with Early Adopters

Large language models (LLMs) like OpenAI ChatGPT, Google Gemini, and GitHub Copilot are rapidly gaining traction in the software industry, but their full impact on software engineering remains insufficiently explored. Despite their growing adoption, there is a notable lack of formal, qualitative assessments of how LLMs are applied in real-world software development contexts. To fill this gap, we conducted semi-structured interviews with sixteen early-adopter professional developers to explore their use of LLMs throughout various stages of the software development life cycle. Our investigation examines four dimensions: people - how LLMs affect individual developers and teams; process - how LLMs alter software engineering workflows; product - LLM impact on software quality and innovation; and society - the broader socioeconomic and ethical implications of LLM adoption. Thematic analysis of our data reveals that while LLMs have not fundamentally revolutionized the development process, they have substantially enhanced routine coding tasks, including code generation, refactoring, and debugging. Developers reported the most effective outcomes when providing LLMs with clear, well-defined problem statements, indicating that LLMs excel with decomposed problems and specific requirements. Furthermore, these early-adopters identified that LLMs offer significant value for personal and professional development, aiding in learning new languages and concepts. Early-adopters, highly skilled in software engineering and how LLMs work, identified early and persisting challenges for software engineering, such as inaccuracies in generated content and the need for careful manual review before integrating LLM outputs into production environments. Our study provides a nuanced understanding of how LLMs are shaping the landscape of software development, with their benefits, limitations, and ongoing implications.