<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>47</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Andrew Sogokon</style></author><author><style face="normal" font="default" size="100%">Khalil Ghorbal</style></author><author><style face="normal" font="default" size="100%">Taylor T. Johnson</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Decoupling Abstractions of Non-linear Ordinary Differential Equations</style></title><secondary-title><style face="normal" font="default" size="100%">FM 2016, 21st International Symposium on Formal Methods</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">abstraction</style></keyword><keyword><style  face="normal" font="default" size="100%">Darboux polynomials</style></keyword><keyword><style  face="normal" font="default" size="100%">decoupling</style></keyword><keyword><style  face="normal" font="default" size="100%">Ordinary differential equations</style></keyword><keyword><style  face="normal" font="default" size="100%">simulation</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">11/2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://link.springer.com/chapter/10.1007/978-3-319-48989-6_38</style></url></web-urls><related-urls><url><style face="normal" font="default" size="100%">https://archive.isis.vanderbilt.edu/sites/default/files/decoupling-abstractions-fm-2016.pdf</style></url></related-urls></urls><publisher><style face="normal" font="default" size="100%">Springer</style></publisher><pub-location><style face="normal" font="default" size="100%">Limassol, Cyprus</style></pub-location><volume><style face="normal" font="default" size="100%">9995 Lecture Notes in Computer Science</style></volume><pages><style face="normal" font="default" size="100%">628-644</style></pages><abstract><style face="normal" font="default" size="100%">We investigate decoupling abstractions, by which we seek to simulate (i.e. abstract) a given system of ordinary differential equations (ODEs) by another system that features completely independent (i.e. uncoupled) sub-systems, which can be considered as separate systems in their own right. Beyond a purely mathematical interest as a tool for the qualitative analysis of ODEs, decoupling can be applied to verification problems arising in the fields of control and hybrid systems. Existing verification technology often scales poorly with dimension. Thus, reducing a verification problem to a number of independent verification problems for systems of smaller dimension may enable one to prove properties that are otherwise seen as too difficult. We show an interesting correspondence between Darboux polynomials and decoupling simulating abstractions of systems of polynomial ODEs and give a constructive procedure for automatically computing the latter.</style></abstract></record></records></xml>