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Instances generation is crucial for linear programming algorithms, which is necessary either to find the optimal pivot rules by training learning method or to evaluate and verify corresponding algorithms. This study proposes a general…
We have developed a symbolic algebra approach to automatically produce, verify, and optimize computer code for the Fast Multipole Method (FMM) operators. This approach allows for flexibility in choosing a basis set and kernel, and can…
Evaluating the correctness of code generated by AI is a challenging open problem. In this paper, we propose a fully automated method, named ACCA, to evaluate the correctness of AI-generated code for security purposes. The method uses…
Loop invariants play a very important role in proving correctness of programs. In this paper, we address the problem of generating invariants of polynomial loop programs. We present a new approach, for generating polynomial equation…
In this work, we study the problem of code generation with a large language model (LLM), with a focus on generating SQL queries from natural language questions. We ask: Instead of using supervised fine tuning with text-code pairs, can we…
The latest paradigm shift in software development brings in the innovation and automation afforded by Large Language Models (LLMs), showcased by Generative Pre-trained Transformer (GPT), which has shown remarkable capacity to generate code…
Several practical tools for automatically verifying functional programs (e.g., Liquid Haskell and Leon for Scala programs) rely on a heuristic based on unrolling recursive function definitions followed by quantifier-free reasoning using SMT…
We report on the automation of a technique to prove the correctness of program transformations in higher-order program calculi which may permit recursive let-bindings as they occur in functional programming languages. A program…
This paper introduces a new storage-optimal first-order method (FOM), CertSDP, for solving a special class of semidefinite programs (SDPs) to high accuracy. The class of SDPs that we consider, the exact QMP-like SDPs, is characterized by…
We present a new method for automatically providing feedback for introductory programming problems. In order to use this method, we need a reference implementation of the assignment, and an error model consisting of potential corrections to…
Recent studies have adopted pre-trained language models, such as CodeT5 and CodeGPT, for automated program generation tasks like code generation, repair, and translation. Numerous language model-based approaches have been proposed and…
Training on verifiable symbolic data is a promising way to expand the reasoning frontier of language models beyond what standard pre-training corpora provide. Yet existing procedural generators often rely on fixed puzzles or templates and…
In this paper, I describe several approaches to automatic or semi-automatic development of symbolic rules for grammar checkers from the information contained in corpora. The rules obtained this way are an important addition to…
Large language models (LLMs), such as GPT-3 and GPT-4, have demonstrated exceptional performance in various natural language processing tasks and have shown the ability to solve certain reasoning problems. However, their reasoning…
This paper obtains a completeness result for inequational reasoning with applicative terms without variables in a setting where the intended semantic models are the full structures, the full type hierarchies over preorders for the base…
Generative models excel at synthesizing high-fidelity samples from complex data distributions, but they often violate hard constraints arising from physical laws or task specifications. A common remedy is to project intermediate samples…
Recent text generation models are easy to generate relevant and fluent text for the given text, while lack of causal reasoning ability when we change some parts of the given text. Counterfactual story rewriting is a recently proposed task…
In the past few years, Large Language Models (LLMs) have exploded in usefulness and popularity for code generation tasks. However, LLMs still struggle with accuracy and are unsuitable for high-risk applications without additional oversight…
The task of generating code solutions for a given programming problem can benefit from the use of pre-trained language models such as Codex, which can produce multiple diverse samples. However, a major challenge for this task is to select…
Automated source code refactoring, particularly extract method refactoring, is a crucial and frequently employed technique during software development. Despite its importance and frequent use by practitioners, current automated techniques…