DeepAI
Log In Sign Up

Certifying Differential Equation Solutions from Computer Algebra Systems in Isabelle/HOL

02/04/2021
by   Thomas Hickman, et al.
0

The Isabelle/HOL proof assistant has a powerful library for continuous analysis, which provides the foundation for verification of hybrid systems. However, Isabelle lacks automated proof support for continuous artifacts, which means that verification is often manual. In contrast, Computer Algebra Systems (CAS), such as Mathematica and SageMath, contain a wealth of efficient algorithms for matrices, differential equations, and other related artifacts. Nevertheless, these algorithms are not verified, and thus their outputs cannot, of themselves, be trusted for use in a safety critical system. In this paper we integrate two CAS systems into Isabelle, with the aim of certifying symbolic solutions to ordinary differential equations. This supports a verification technique that is both automated and trustworthy.

READ FULL TEXT
02/13/2017

Algorithmic Verification of Linearizability for Ordinary Differential Equations

For a nonlinear ordinary differential equation solved with respect to th...
09/19/2017

Synthesizing SystemC Code from Delay Hybrid CSP

Delay is omnipresent in modern control systems, which can prompt oscilla...
02/11/2022

Formal verification of iterative convergence of numerical algorithms

Physical systems are usually modeled by differential equations, but solv...
04/16/2019

An Axiomatic Approach to Liveness for Differential Equations

This paper presents an approach for deductive liveness verification for ...
05/27/2016

Numeric Deduction in Symbolic Computation. Application to Normalizing Transformations

Algorithms of numeric (in exact arithmetic) deduction of analytical expr...
07/14/2022

Learning port-Hamiltonian systems – algorithms

In this article we study the possibilities of recovering the structure o...
09/18/2021

Automated Symbolic and Numerical Testing of DLMF Formulae using Computer Algebra Systems

We have developed an automated procedure for symbolic and numerical test...