Related papers: Machine-Verifying Toom-Cook Multiplication with In…
This paper considers the development of an AI-based provably-correct mathematical proof tutor. While Large Language Models (LLMs) allow seamless communication in natural language, they are error prone. Theorem provers such as Lean allow for…
The advent of large language models trained on code (code LLMs) has led to significant progress in language-to-code generation. State-of-the-art approaches in this area combine LLM decoding with sample pruning and reranking using test cases…
The proliferation of cloud computing technologies has paved the way for deploying networked encrypted control systems, offering high performance, remote accessibility and privacy. However, in scenarios where the control algorithms run on…
Quantum process tomography is a necessary tool for verifying quantum gates and diagnosing faults in architectures and gate design. We show that the standard approach of process tomography is grossly inaccurate in the case where the states…
Large computer-understandable proofs consist of millions of intermediate logical steps. The vast majority of such steps originate from manually selected and manually guided heuristics applied to intermediate goals. So far, machine learning…
Computer-based systems have been used to solve several domain problems, such as industrial, military, education, and wearable. Those systems need high-quality software to guarantee security and safety. We advocate that Bounded Model…
The general-purpose interactive theorem-proving assistant called Prove-It was used to verify the Quantum Phase Estimation (QPE) algorithm, specifically claims about its outcome probabilities. Prove-It is unique in its ability to express…
Large Language Models (LLMs) can generate useful code, but often the code they generate cannot be trusted to be sound. In this paper, we present VerMCTS, an approach to begin to resolve this issue by generating verified programs in Dafny…
Being able to soundly estimate roundoff errors of finite-precision computations is important for many applications in embedded systems and scientific computing. Due to the discrepancy between continuous reals and discrete finite-precision…
We describe a general and safe computational framework that provides integer programming results with the degree of certainty that is required for machine-assisted proofs of mathematical theorems. At its core, the framework relies on a…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
Fault-tolerant quantum computation using lattice surgery can be abstracted as operations on graphs, wherein each logical qubit corresponds to a vertex of the graph, and multi-qubit measurements are accomplished by connecting the vertices…
The points-to problem is the problem of determining the possible run-time targets of pointer variables and is usually considered part of the more general aliasing problem, which consists in establishing whether and when different…
Proof automation is crucial to large-scale formal mathematics and software/hardware verification projects in ITPs. Sophisticated tools called hammers have been developed to provide general-purpose proof automation in ITPs such as Coq and…
Automated theorem proving has long been a key task of artificial intelligence. Proofs form the bedrock of rigorous scientific inquiry. Many tools for both partially and fully automating their derivations have been developed over the last…
Recent advances have shown that scaling test-time computation enables large language models (LLMs) to solve increasingly complex problems across diverse domains. One effective paradigm for test-time scaling (TTS) involves LLM generators…
Verifying whether a procedure is observationally pure is useful in many software engineering scenarios. An observationally pure procedure always returns the same value for the same argument, and thus mimics a mathematical function. The…
We present two new positive results for reliable computation using formulas over physical alphabets of size $q > 2$. First, we show that for logical alphabets of size $\ell = q$ the threshold for denoising using gates subject to $q$-ary…
With the rapid advancement of test-time compute search strategies to improve the mathematical problem-solving capabilities of large language models (LLMs), the need for building robust verifiers has become increasingly important. However,…
While Chain-of-Thought (CoT) prompting enhances the reasoning capabilities of large language models, the faithfulness of the generated rationales remains an open problem for model interpretability. We propose a novel theoretical lens for…