相关论文: Verified Real Number Calculations: A Library for I…

Numerical reasoning is vital for natural language processing models to understand and process numerical information in real-world scenarios. Most current methods first generate the Intermediate Meaning Representations (IMRs) of questions…

Computers calculate transcendental functions by approximating them through the composition of a few limited-precision instructions. For example, an exponential can be calculated with a Taylor series. These approximation methods were…

Large-scale computer experiments are becoming increasingly important in science. A multi-step procedure is introduced to statisticians for modeling such experiments, which builds an accurate interpolator in multiple steps. In practice, the…

We propose here a number of approaches to implement constraint propagation for arithmetic constraints on integer intervals. To this end we introduce integer interval arithmetic. Each approach is explained using appropriate proof rules that…

AI agents have shown initial promise in automating mathematical theorem proving in proof assistants such as Lean. The same proof assistants can be used to verify the correctness of code by pairing code with specifications and proofs that…

Interval arithmetic is hardly feasible without directed rounding as provided, for example, by the IEEE floating-point standard. Equally essential for interval methods is directed rounding for conversion between the external decimal and…

A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…

Automated theorem proving, or more broadly automated reasoning, aims at using computer programs to automatically prove or disprove mathematical theorems and logical statements. It takes on an essential role across a vast array of…

This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic…

We give a process for verifying numerical programs against their functional specifications. Our implementation is capable of automatically verifying programs against tight error bounds featuring common elementary functions. We demonstrate…

Elfe is an interactive system for teaching basic proof methods in discrete mathematics. The user inputs a mathematical text written in fair English which is converted to a special data-structure of first-order formulas. Certain proof…

Theorem proving is a fundamental aspect of mathematics, spanning from informal reasoning in natural language to rigorous derivations in formal systems. In recent years, the advancement of deep learning, especially the emergence of large…

Research project "Platform-independent approach to formal specification and verification of standard mathematical functions" is aimed onto a development of an incremental combined approach to the specification and verification of the…

We show how to represent an interval of real numbers in an abstract numeration system built on a language that is not necessarily regular. As an application, we consider representations of real numbers using the Dyck language. We also show…

Proving lemmas in synthetic geometry is often a time-consuming endeavour since many intermediate lemmas need to be proven before interesting results can be obtained. Improvements in automated theorem provers (ATP) in recent years now mean…

Verifying mathematical proofs is difficult, but can be automated with the assistance of a computer. Autoformalization is the task of automatically translating natural language mathematics into a formal language that can be verified by a…

Arithmetic constraints on integer intervals are supported in many constraint programming systems. We study here a number of approaches to implement constraint propagation for these constraints. To describe them we introduce integer interval…

We present StepFun-Prover Preview, a large language model designed for formal theorem proving through tool-integrated reasoning. Using a reinforcement learning pipeline that incorporates tool-based interactions, StepFun-Prover can achieve…

Recently, there has been considerable progress on designing algorithms with provable guarantees -- typically using linear algebraic methods -- for parameter learning in latent variable models. But designing provable algorithms for inference…

An invaluable feature of computer algebra systems is their ability to plot the graph of functions. Unfortunately, when one is trying to design a library of mathematical functions, this feature often falls short, producing incorrect and…