Related papers: Implementation and Synthesis of Math Library Funct…
Following in the footsteps of the success of Mathlib - the centralised library of formalised mathematics in Lean - CSLib is a rapidly-growing centralised library of formalised computer science and software. In this paper, we present its…
We present \synver{}, a novel synthesis and verification framework for C programs, that deploys a Large Language Model (LLM) to search for a candidate program that satisfies the given specification. Our key idea is to impose syntactic and…
Linear algebra is a major field of numerical computation and is widely applied. Most linear algebra libraries (in most programming languages) do not statically guarantee consistency of the dimensions of vectors and matrices, causing runtime…
Large Language Models (LLMs) have demonstrated remarkable capabilities across a wide range of natural language processing and reasoning tasks. However, their performance in the foundational domain of arithmetic remains unsatisfactory. When…
Codifying mathematical theories in a proof assistant or computer algebra system is a challenging task, of which the most difficult part is, counterintuitively, structuring definitions. This results in a steep learning curve for new users…
Despite great advances in program synthesis techniques, they remain algorithmic black boxes. Although they guarantee that when synthesis is successful, the implementation satisfies the specification, they provide no additional information…
Despite significant advancements in text generation and reasoning, Large Language Models (LLMs) still face challenges in accurately performing complex arithmetic operations. Language model systems often enable LLMs to generate code for…
Recent advancements in large language models (LLMs) have showcased significant improvements in mathematics. However, traditional math benchmarks like GSM8k offer a unidimensional perspective, falling short in providing a holistic assessment…
Mathematical programming -- the task of expressing operations and decision-making problems in precise mathematical language -- is fundamental across domains, yet remains a skill-intensive process requiring operations research expertise.…
We present solidfmm, a highly optimised C++ library for the solid harmonics as they are needed in fast multipole methods. The library provides efficient, vectorised implementations of the translation operations M2M, M2L, and L2L, and is…
Recent frontier-level LLMs have saturated many previously difficult benchmarks, leaving little room for further differentiation. This progress highlights the need for challenging benchmarks that provide objective verification. In this…
As computational challenges in optimization and statistical inference grow ever harder, algorithms that utilize derivatives are becoming increasingly more important. The implementation of the derivatives that make these algorithms so…
Logic synthesis is a fundamental step in hardware design whose goal is to find structural representations of Boolean functions while minimizing delay and area. If the function is completely-specified, the implementation accurately…
The mathematical capabilities of Multi-modal Large Language Models (MLLMs) remain under-explored with three areas to be improved: visual encoding of math diagrams, diagram-language alignment, and chain-of-thought (CoT) reasoning. This draws…
Mata is a well-engineered automata library written in C++ that offers a unique combination of speed and simplicity. It is meant to serve in applications such as string constraint solving and reasoning about regular expressions, and as…
Whenever a bug occurs in a program, software developers assume that the code is flawed, not the compiler. In fact, if compilers should be correct, they are just normal software with their own bugs. Hard to find, errors in them have…
We describe lrsarith which is a small fixed precision and hybrid arithmetic C library for integers and rationals that we developed for use in the lrslib library for polyhedral computation. Using a generic set of operations, a program can be…
Current compiler optimization reports often present complex, technical information that is difficult for programmers to interpret and act upon effectively. This paper assesses the capability of large language models (LLM) to understand…
High computation costs and latency of large language models such as GPT-4 have limited their deployment in clinical settings. Small language models (SLMs) offer a cost-effective alternative, but their limited capacity requires biomedical…
Code bloat widely exists in production-run software. Left untackled, it not only degrades software performance but also increases its attack surface. In this work, we conduct a case study to understand this issue in statically linked…