Inspired by the pedagogical method of "proof by counterexamples" widely used in human mathematics education, our work aims to enhance Large Language Models’ (LLMs) ability to conduct mathematical ...

Mathematical Large Language Models (LLMs) have demonstrated strong problem-solving capabilities, but their reasoning ability is often constrained by pattern recognition rather than true conceptual ...

This is a preview. Log in through your library . Abstract We construct a counterexample to the "hot spots" conjecture; there exists a bounded connected planar domain (with two holes) such that the ...

This is a preview. Log in through your library . Abstract We answer an old question due to Kuratowski by constructing a (separable metric) space X having the ...

Abstract: Motivated by the presence of an implicit communication channel in the asymptotic version of Witsenhausen's counterexample, implicit discrete memoryless channels (IDMC) with discrete ...

Abstract: Directed fuzzing demonstrates the potential to reproduce bug reports, verify patches, and debug vulnerabilities. State-of-the-art directed fuzzers prioritize inputs that are more likely to ...