相关论文: Goedel Machines: Self-Referential Universal Proble…
Program analysis and verification require decision procedures to reason on theories of data structures. Many problems can be reduced to the satisfiability of sets of ground literals in theory T. If a sound and complete inference system for…
Convex optimization problems with staged structure appear in several contexts, including optimal control, verification of deep neural networks, and isotonic regression. Off-the-shelf solvers can solve these problems but may scale poorly. We…
We introduce the Rebound library that supports well-scoped term representations in Haskell and automates the definition of substitution, alpha-equivalence, and other operations that work with binding structures. The key idea of our design…
This chapter provides a hands-on tutorial on the important technique known as self-reducibility. Through a series of "Challenge Problems" that are theorems that the reader will---after being given definitions and tools---try to prove, the…
Like humans, large language models (LLMs) do not always generate the best output on their first try. Motivated by how humans refine their written text, we introduce Self-Refine, an approach for improving initial outputs from LLMs through…
An efficient and flexible engine for computing fixed points is critical for many practical applications. In this paper, we firstly present a goal-directed fixed point computation strategy in the logic programming paradigm. The strategy…
Mechanized theorem proving is becoming the basis of reliable systems programming and rigorous mathematics. Despite decades of progress in proof automation, writing mechanized proofs still requires engineers' expertise and remains labor…
In this paper, we propose a new concept called \textit{semantically equivalence} \wrt \textit{optimization phases} \textit{(\sep)}, which defines the set of programs a compiler considers semantically equivalent to the input using a set of…
Research must be reproducible in order to make an impact on science and to contribute to the body of knowledge in our field. Yet studies have shown that 70% of research from academic labs cannot be reproduced. In software engineering, and…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
To solve Math Word Problems, human students leverage diverse reasoning logic that reaches different possible equation solutions. However, the mainstream sequence-to-sequence approach of automatic solvers aims to decode a fixed solution…
Generating high-quality code that solves complex programming tasks is challenging, especially with current decoder-based models that produce highly stochastic outputs. In code generation, even minor errors can easily break the entire…
A self-corrector for a function $f$ takes a black-box oracle computing $f$ that is correct on most inputs and turns it into one that is correct on every input with high probability. Self-correctors exist for any function that is randomly…
A new viewpoint of the G\"odel's incompleteness theorem be given in this article which reveals the deep relationship between the logic and computation. Upon the results of these studies, an algorithm be given which shows how to search a…
An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…
Advanced test-time computing strategies are essential for scaling reasoning models, but their effectiveness is capped by the models' poor self-evaluation. We propose a pairwise Explanatory Verifier, trained via reinforcement learning…
Mathematical theorems are human knowledge able to be accumulated in the form of symbolic representation, and proving theorems has been considered intelligent behavior. Based on the BHK interpretation and the Curry-Howard isomorphism, proof…
This paper investigates a category of constrained fractional optimization problems that emerge in various practical applications. The objective function for this category is characterized by the ratio of a numerator and denominator, both…
Traditional retrieval methods rely on transforming user queries into vector representations and retrieving documents based on cosine similarity within an embedding space. While efficient and scalable, this approach often fails to handle…
Inductive theorem proving is an important long-standing challenge in computer science. In this extended abstract, we first summarize the recent developments of proof by induction for Isabelle/HOL. Then, we propose united reasoning, a novel…