Related papers: A Macro for Reusing Abstract Functions and Theorem…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
The use of approximation is fundamental in computational science. Almost all computational methods adopt approximations in some form in order to obtain a favourable cost/accuracy trade-off and there are usually many approximations that…
The task of inferring logical formulas from examples has garnered significant attention as a means to assist engineers in creating formal specifications used in the design, synthesis, and verification of computing systems. Among various…
Reproducibility of computational results remains a challenge in materials science, as simulation workflows and parameters are often reported only in unstructured text and tables. While literature data are valuable for validation and reuse,…
We propose a method for automatically generating abstract transformers for static analysis by abstract interpretation. The method focuses on linear constraints on programs operating on rational, real or floating-point variables and…
The complexity of large-scale distributed systems, particularly when deployed in physical space, calls for new mechanisms to address composability and reusability of collective adaptive behaviour. Computational fields have been proposed as…
With the increasing ability of large language models (LLMs), in-context learning (ICL) has evolved as a new paradigm for natural language processing (NLP), where instead of fine-tuning the parameters of an LLM specific to a downstream task…
We present a novel technique for combining statistical machine learning for proof-pattern recognition with symbolic methods for lemma discovery. The resulting tool, ACL2(ml), gathers proof statistics and uses statistical pattern-recognition…
Recent advances in large language models (LLMs) have shown that Chain-of-Thought (CoT) reasoning can substantially improve performance on complex reasoning tasks. At the same time, In-Context Learning (ICL) has become an important mechanism…
Continual learning and few-shot learning are important frontiers in progress toward broader Machine Learning (ML) capabilities. Recently, there has been intense interest in combining both. One of the first examples to do so was the…
The Abstraction and Reasoning Corpus (ARC) poses a significant challenge to artificial intelligence, demanding broad generalization and few-shot learning capabilities that remain elusive for current deep learning methods, including large…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…
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…
Large language models (LLMs) have shown promising performance across diverse domains. Many practical applications of LLMs, such as code completion and structured data extraction, require adherence to syntactic constraints specified by a…
Recent advances in large language models (LLMs) have revolutionized the landscape of reasoning tasks. To enhance the capabilities of LLMs to emulate human reasoning, prior studies have focused on modeling reasoning steps using various…
Large Language Models (LLMs) have demonstrated the ability to solve complex tasks through In-Context Learning (ICL), where models learn from a few input-output pairs without explicit fine-tuning. In this paper, we explore the capacity of…
We propose an operationally-based deductive proof method for program equivalence. It is based on encoding the language semantics as logically constrained term rewriting systems (LCTRSs) and the two programs as terms. The main feature of our…
In a previous paper [Adcock & Huybrechs, 2019] we described the numerical approximation of functions using redundant sets and frames. Redundancy in the function representation offers enormous flexibility compared to using a basis, but…
The detection of allusive text reuse is particularly challenging due to the sparse evidence on which allusive references rely---commonly based on none or very few shared words. Arguably, lexical semantics can be resorted to since uncovering…
We report on our experience using ACL2 in the classroom to teach students about software testing. The course COSC2300 at the University of Wyoming is a mostly traditional Discrete Mathematics course, but with a clear focus on computer…