相关论文: Computer validated proofs of a toolset for adaptab…

Teaching precise mathematical reasoning can be very hard. It is very easy for a student to make a subtle mistake in a proof which invalidates it, but it is often hard for the teacher to pinpoint and explain the problem in the (often…

Software for mixed-integer linear programming can return incorrect results for a number of reasons, one being the use of inexact floating-point arithmetic. Even solvers that employ exact arithmetic may suffer from programming or algorithmic…

Approximate computing (AC) is an emerging paradigm for energy-efficient computation. The basic idea of AC is to sacrifice high precision for low energy by allowing for hardware which only carries out "approximately correct" calculations.…

Real number calculations on elementary functions are remarkably difficult to handle in mechanical proofs. In this paper, we show how these calculations can be performed within a theorem prover or proof assistant in a convenient and highly…

Core-sets refer to subsets of data that maximize some function that is commonly a diversity or group requirement. These subsets are used in place of the original data to accomplish a given task with comparable or even enhanced performance…

A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid excessive rounding error propagation of conventional…

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 work, we describe our experience in learning the use of a computer proof assistant - specifically, Lean - from scratch, through proving formulae for the solutions of polynomial equations. Specifically, in this work we characterize…

Floating point operations are fast, but require continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the user by providing a library of exact analysis in which the…

We describe how we connected three programs that compute Groebner bases to Coq, to do automated proofs on algebraic, geometrical and arithmetical expressions. The result is a set of Coq tactics and a certificate mechanism (downloadable at…

Virtual integration techniques focus on building architectural models of systems that can be analyzed early in the design cycle to try to lower cost, reduce risk, and improve quality of complex embedded systems. Given appropriate…

Cody & Waite argument reduction technique works perfectly for reasonably large arguments but as the input grows there are no bit left to approximate the constant with enough accuracy. Under mild assumptions, we show that the result computed…

Theorem provers are important tools for people working in formal verification. There are a myriad of interactive systems available today, with varying features and approaches motivating their development. These design choices impact their…

Numerical accuracy of floating point computation is a well studied topic which has not made its way to the end-user in scientific computing. Yet, it has become a critical issue with the recent requirements for code modernization to harness…

The traditional foundation of science lies on the cornerstones of theory and experiment. Theory is used to explain experiment, which in turn guides the development of theory. Since the advent of computers and the development of…

In this paper we give a preliminary formalization of the p-adic numbers, in the context of the second author's univalent foundations program. We also provide the corresponding code verifying the construction in the proof assistant Coq.…

We formally verify an algorithm for approximate policy iteration on Factored Markov Decision Processes using the interactive theorem prover Isabelle/HOL. Next, we show how the formalized algorithm can be refined to an executable, verified…

We describe a general and safe computational framework that provides integer programming results with the degree of certainty that is required for machine-assisted proofs of mathematical theorems. At its core, the framework relies on a…

Proust is a small Racket program offering rudimentary interactive assistance in the development of verified proofs for propositional and predicate logic. It is constructed in stages, some of which are done by students before using it to…

Formal program verification is a longstanding goal in the field. We present the first quantitative comparison of the two primary compiler verification approaches, credible compilation/translation validation and full verification. Working…