Related papers: The Boyer-Moore Waterfall Model Revisited
Artificial intelligence assisted mathematical proof has become a highly focused area nowadays. One key problem in this field is to generate formal mathematical proofs from natural language proofs. Due to historical reasons, the formal proof…
We propose ProofNet++, a neuro-symbolic framework that enhances automated theorem proving by combining large language models (LLMs) with formal proof verification and self-correction mechanisms. Current LLM-based systems suffer from…
A new method for document watermarking based on the digital Fourier hologram is proposed. It applies the methods of digital image watermarking based on holographic principle presented previously in several papers into printed documents.…
Watermarking for large language models (LLMs) has emerged as an effective tool for distinguishing AI-generated text from human-written content. Statistically, watermark schemes induce dependence between generated tokens and a pseudo-random…
Lean is an increasingly popular proof assistant based on dependent type theory. Despite its success, it still lacks important automation features present in more seasoned proof assistants, such as the Sledgehammer tactic in Isabelle/HOL. A…
Learning-assisted automated reasoning has recently gained popularity among the users of Isabelle/HOL, HOL Light, and Mizar. In this paper, we present an add-on to the HOL4 proof assistant and an adaptation of the HOLyHammer system that…
Formal reasoning and automated theorem proving constitute a challenging subfield of machine learning, in which machines are tasked with proving mathematical theorems using formal languages like Lean. A formal verification system can check…
The application of automatic theorem provers to discharge proof obligations is necessary to apply formal methods in an efficient manner. Tools supporting formal methods, such as Atelier~B, generate proof obligations fully automatically.…
This work presents a formalized proof of modal completeness for G\"odel-L\"ob provability logic (GL) in the HOL Light theorem prover. We describe the code we developed, and discuss some details of our implementation, focusing on our choices…
The automation offered by modern program proof tools goes hand in hand with the capability to interact with the tool when the verification fails. The SPARK proof tool tries to help the user by providing the right information, so that the…
Deciding which sub-tool to use for a given proof state requires expertise specific to each ITP. To mitigate this problem, we present PaMpeR, a Proof Method Recommendation system for Isabelle/HOL. Given a proof state, PaMpeR recommends proof…
LLM watermarks stand out as a promising way to attribute ownership of LLM-generated text. One threat to watermark credibility comes from spoofing attacks, where an unauthorized third party forges the watermark, enabling it to falsely…
Ackermann's function can be expressed using an iterative algorithm, which essentially takes the form of a term rewriting system. Although the termination of this algorithm is far from obvious, its equivalence to the traditional recursive…
Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today's powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search,…
Theorem proving serves as a major testbed for evaluating complex reasoning abilities in large language models (LLMs). However, traditional automated theorem proving (ATP) approaches rely heavily on formal proof systems that poorly align…
Machine-assisted theorem proving refers to the process of conducting structured reasoning to automatically generate proofs for mathematical theorems. Recently, there has been a surge of interest in using machine learning models in…
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…
We propose a new algorithm for computing validated bounds for the solutions to the first order variational equations associated to ODEs. These validated solutions are the kernel of numerics computer-assisted proofs in dynamical systems…
Interactive proof assistants make it possible for ordinary mathematicians to write definitions and theorems in a formal proof language, like a programming language, so that a computer can parse them and check them against the rules of a…
In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…