Related papers: Verified AIG Algorithms in ACL2
There has been a surge in Explainable-AI (XAI) methods that provide insights into the workings of Deep Neural Network (DNN) models. Integrated Gradients (IG) is a popular XAI algorithm that attributes relevance scores to input features…
Graph neural networks (GNNs) are increasingly often employed in high-stakes applications, such as fraud detection or healthcare, but are susceptible to adversarial attacks. A number of techniques have been proposed to provide adversarial…
Large language models (LLMs) have exhibited remarkable capabilities in text generation tasks. However, the utilization of these models carries inherent risks, including but not limited to plagiarism, the dissemination of fake news, and…
Domain of mathematical logic in computers is dominated by automated theorem provers (ATP) and interactive theorem provers (ITP). Both of these are hard to access by AI from the human-imitation approach: ATPs often use human-unfriendly…
We study the synthesis of circuits for succinct safety specifications given in the AIG format. We show how AIG safety specifications can be decomposed automatically into sub specifications. Then we propose symbolic compositional algorithms…
The Boolean circuit simplification problem involves finding a smaller circuit that computes the same function as a given Boolean circuit. This problem is closely related to several key areas with both theoretical and practical applications,…
Algebraic Multigrid (AMG) methods are often robust and effective solvers for solving the large and sparse linear systems that arise from discretized PDEs and other problems, relying on heuristic graph algorithms to achieve their…
Clausal proofs have become a popular approach to validate the results of SAT solvers. However, validating clausal proofs in the most widely supported format (DRAT) is expensive even in highly optimized implementations. We present a new…
The theory of asymptotic complexity provides an approach to characterizing the behavior of programs in terms of bounds on the number of computational steps executed or use of computational resources. We describe work using ACL2 to prove…
Proving the correctness of programs written for multiple processors is a challenging problem, due in no small part to the weaker memory guarantees afforded by most modern architectures. In particular, the existence of store buffers means…
FGL is a successor to GL, a proof procedure for ACL2 that allows complicated finitary conjectures to be translated into efficient Boolean function representations and proved using SAT solvers. A primary focus of FGL is to allow greater…
Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms…
We present ProvG-Searcher, a novel approach for detecting known APT behaviors within system security logs. Our approach leverages provenance graphs, a comprehensive graph representation of event logs, to capture and depict data provenance…
Understanding the structure and function of circuits is crucial for electronic design automation (EDA). Circuits can be formulated as And-Inverter graphs (AIGs), enabling efficient implementation of representation learning through graph…
This paper proposes Inverse Gram Matrix (IGM) methods to prioritize the Pairwise Reciprocal Matrix (PRM) in the Analytic Hierarchy Process. The IGM methods include Pseudo-IGM, Normalized-IGM, and Lagrange-IGM. Interestingly, the proposed…
Algebraic multigrid (AMG) solvers and preconditioners are some of the fastest numerical methods to solve linear systems, particularly in a parallel environment, scaling to hundreds of thousands of cores. Most AMG methods and theory assume a…
We present a tool, simplify-defun, that transforms the definition of a given function into a simplified definition of a new function, providing a proof checked by ACL2 that the old and new functions are equivalent. When appropriate it also…
In our current work a library of formally verified software components is to be created, and assembled, using the Low-Level Virtual Machine (LLVM) intermediate form, into subsystems whose top-level assurance relies on the assurance of the…
This study evaluates AoS-to-SoA transformations over reduced-precision data layouts for a particle simulation code on several GPU platforms: We hypothesize that SoA fits particularly well to SIMT, while AoS is the preferred storage format…
Self-supervised learning (SSL) with vision transformers (ViTs) has proven effective for representation learning as demonstrated by the impressive performance on various downstream tasks. Despite these successes, existing ViT-based SSL…