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Whether LLMs can reason or write software is widely debated, but whether they can write software that itself reasons is largely unexplored. We present a case study in which an LLM coding agent builds a complete DPLL(T)-style SMT solver for…

Logic in Computer Science · Computer Science 2026-03-11 Mikoláš Janota , Mirek Olšák

Large Language Models (LLMs) have shown remarkable success on a wide range of math and reasoning benchmarks. However, we observe that they often struggle when faced with unreasonable math problems. Instead of recognizing these issues,…

Computation and Language · Computer Science 2025-06-03 Jingyuan Ma , Damai Dai , Zihang Yuan , Rui li , Weilin Luo , Bin Wang , Qun Liu , Lei Sha , Zhifang Sui

Large language models (LLMs) are increasingly deployed on complex reasoning tasks, yet little is known about their ability to internally evaluate problem difficulty, which is an essential capability for adaptive reasoning and efficient…

Computation and Language · Computer Science 2025-10-14 Sunbowen Lee , Qingyu Yin , Chak Tou Leong , Jialiang Zhang , Yicheng Gong , Shiwen Ni , Min Yang , Xiaoyu Shen

Large Language Models are increasingly used by students to explore advanced material in computer science, including graph theory. As these tools become integrated into undergraduate and graduate coursework, it is important to understand how…

Artificial Intelligence · Computer Science 2026-02-06 Adithya Kulkarni , Mohna Chakraborty , Jay Bagga

We present AMO-Bench, an Advanced Mathematical reasoning benchmark with Olympiad level or even higher difficulty, comprising 50 human-crafted problems. Existing benchmarks have widely leveraged high school math competitions for evaluating…

Computation and Language · Computer Science 2025-10-31 Shengnan An , Xunliang Cai , Xuezhi Cao , Xiaoyu Li , Yehao Lin , Junlin Liu , Xinxuan Lv , Dan Ma , Xuanlin Wang , Ziwen Wang , Shuang Zhou

The evolution of mathematics is shaped importantly by interestingness: researchers choose which problems to pursue, and students choose which problems to engage with, based on expectations of interest and challenge. As AI systems,…

Computing olympiads contain some of the most challenging problems for humans, requiring complex algorithmic reasoning, puzzle solving, in addition to generating efficient code. However, it has been understudied as a domain to evaluate…

Computation and Language · Computer Science 2024-04-18 Quan Shi , Michael Tang , Karthik Narasimhan , Shunyu Yao

Determining whether a program terminates is a central problem in computer science. Turing's Halting Problem established termination as undecidable, showing that no algorithm can universally determine termination for all programs and inputs.…

Computation and Language · Computer Science 2026-05-27 Oren Sultan , Jordi Armengol-Estape , Pascal Kesseli , Julien Vanegue , Dafna Shahaf , Yossi Adi , Peter O'Hearn

The motivation of this work is to illustrate the efficiency of some often overlooked alternatives to deal with optimization problems in systems and control. In particular, we will consider a problem for which an iterative linear matrix…

Optimization and Control · Mathematics 2011-07-05 Emile Simon , Vincent Wertz

Although demonstrating remarkable performance on reasoning tasks, Large Language Models (LLMs) still tend to fabricate unreliable responses when confronted with problems that are unsolvable or beyond their capability, severely undermining…

Computation and Language · Computer Science 2025-11-13 Boyang Xue , Qi Zhu , Rui Wang , Sheng Wang , Hongru Wang , Minda Hu , Fei Mi , Yasheng Wang , Lifeng Shang , Qun Liu , Kam-Fai Wong

Recent math benchmarks for large language models (LLMs) such as MathArena indicate that state-of-the-art reasoning models achieve impressive performance on mathematical competitions like AIME, with the leading model, Gemini-2.5-Pro,…

Large language models (LLMs) have exhibited impressive capabilities in comprehending complex instructions. However, their blind adherence to provided instructions has led to concerns regarding risks of malicious use. Existing defence…

Artificial Intelligence · Computer Science 2023-07-25 David Glukhov , Ilia Shumailov , Yarin Gal , Nicolas Papernot , Vardan Papyan

Recent reports claim that large language models (LLMs) now outperform elite humans in competitive programming. Drawing on knowledge from a group of medalists in international algorithmic contests, we revisit this claim, examining how LLMs…

Among the hardest tasks for humans are those found in competitive programming where problems require sophisticated algorithmic thinking, puzzle solving, and the creation of effective code. As a domain to assess language models (LMs), it has…

Computation and Language · Computer Science 2025-09-03 Md Tanzib Hosain , Md Kishor Morol

Advanced applied mathematics problems are underrepresented in existing Large Language Model (LLM) benchmark datasets. To address this, we introduce HARDMath, a dataset inspired by a graduate course on asymptotic methods, featuring…

Fermi Problems (FPs) are mathematical reasoning tasks that require human-like logic and numerical reasoning. Unlike other reasoning questions, FPs often involve real-world impracticalities or ambiguous concepts, making them challenging even…

Computation and Language · Computer Science 2025-04-04 Zishuo Liu , Carlos Rabat Villarreal , Mostafa Rahgouy , Amit Das , Zheng Zhang , Chang Ren , Dongji Feng

Large language models (LLMs) have significantly advanced natural language understanding and demonstrated strong problem-solving abilities. Despite these successes, most LLMs still struggle with solving mathematical problems due to the…

Computation and Language · Computer Science 2024-06-27 Meng Fang , Xiangpeng Wan , Fei Lu , Fei Xing , Kai Zou

Majority voting over multiple LLM attempts improves mathematical reasoning, but correlated errors limit the effective sample size. A natural fix is to assign different reasoning strategies to different voters. The approach, Diverse Prompt…

Computation and Language · Computer Science 2026-04-17 Natapong Nitarach

We study the depth of grade-school math (GSM) problem-solving capabilities of LLMs. To this end, we evaluate their performance on pairs of existing math word problems together so that the answer to the second problem depends on correctly…

Machine Learning · Computer Science 2024-10-03 Arian Hosseini , Alessandro Sordoni , Daniel Toyama , Aaron Courville , Rishabh Agarwal

This paper investigates the mathematical reasoning capabilities of large language models (LLMs) using 50 newly constructed high-school-level word problems. Unlike prior studies that focus solely on answer correctness, we rigorously analyze…

Artificial Intelligence · Computer Science 2025-02-24 Johan Boye , Birger Moell