Related papers: A Formally Verified Procedure for Width Inference …

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…

Partial differential equations describing the dynamics of physical systems rarely have closed-form solutions. Fourier spectral methods, which use Fast Fourier Transforms (FFTs) to approximate solutions, are a common approach to solving…

Verifying relations between programs arises as a task in various verification contexts such as optimizing transformations, relating new versions of programs with older versions (regression verification), and noninterference. However,…

We present a formal tool for verification of multivariate nonlinear inequalities. Our verification method is based on interval arithmetic with Taylor approximations. Our tool is implemented in the HOL Light proof assistant and it is capable…

Language models that can learn a task at inference time, called in-context learning (ICL), show increasing promise in natural language inference tasks. In ICL, a model user constructs a prompt to describe a task with a natural language…

Fill-in-the-Middle (FIM) is a common pretraining method for code LLMs, where models complete code segments given surrounding context. However, existing LLMs treat code as plain text and mask random character spans. We propose and evaluate…

The Check tools automate formal memory consistency model and security verification of processors by analyzing abstract models of microarchitectures, called $\mu$SPEC models. Despite the efficacy of this approach, a verification gap between…

Bug reproduction is critical in the software debugging and repair process, yet the majority of bugs in open-source and industrial settings lack executable tests to reproduce them at the time they are reported, making diagnosis and…

We consider the feasibility problem of integer linear programming (ILP). We show that solutions of any ILP instance can be naturally represented by an FO-definable class of graphs. For each solution there may be many graphs representing it.…

The use of intrinsic functions to leverage hardware-specific capabilities is a crucial approach for optimizing library performance. Many mainstream libraries implement a large number of vectorized algorithms on Arm or x86 SIMD…

In recent years it has turned out that shearlets have the potential to retrieve directional information so that they became interesting for many applications. Moreover the continuous shearlet transform has the outstanding property to stem…

Context. Filamentary structures appear to be ubiquitous in the interstellar medium. Being able to detect and characterize them is the first step toward understanding their origin, their evolution, and their role in the Galactic cycle of…

In this work, we study linear error-correcting codes against adversarial insertion-deletion (indel) errors. While most constructions for the indel model are nonlinear, linear codes offer compact representations, efficient encoding, and…

Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance for FPGAs…

This is the first paper in a series of work we have accomplished over the past three years. In this paper, we have constructed a consistent formal plane geometry system. This will serve as a crucial bridge between IMO-level plane geometry…

Network protocol parsers are essential for enabling correct and secure communication between devices. Bugs in these parsers can introduce critical vulnerabilities, including memory corruption, information leakage, and denial-of-service…

We present Wildflare GuardRail, a guardrail pipeline designed to enhance the safety and reliability of Large Language Model (LLM) inferences by systematically addressing risks across the entire processing workflow. Wildflare GuardRail…

Let insertion in program generation is producing code with definitions (let-statements). Although definitions precede uses in generated code, during code generation `uses' come first: we might not even know a definition is needed until we…

Large Language Models (LLMs) have demonstrated remarkable potential in hardware front-end design using hardware description languages (HDLs). However, their inherent tendency toward hallucination often introduces functional errors into the…

Albeit being a central notion of every programming language, formally and modularly reasoning about iteration proves itself to be a non-trivial feat, specially in the context of higher-order iteration. In this paper, we present a generic…