1.0Microsoft Researchhttps://www.microsoft.com/en-us/researchSumit Gulwanihttps://www.microsoft.com/en-us/research/people/sumitg/rich600338<blockquote class="wp-embedded-content" data-secret="n5k2s32c0N"><a href="https://www.microsoft.com/en-us/research/publication/continuity-robustness-programs/">Continuity and Robustness of Programs</a></blockquote><iframe sandbox="allow-scripts" security="restricted" src="https://www.microsoft.com/en-us/research/publication/continuity-robustness-programs/embed/#?secret=n5k2s32c0N" width="600" height="338" title="“Continuity and Robustness of Programs” — Microsoft Research" data-secret="n5k2s32c0N" frameborder="0" marginwidth="0" marginheight="0" scrolling="no" class="wp-embedded-content"></iframe><script type="text/javascript"> /* <![CDATA[ */ /*! This file is auto-generated */ !function(d,l){"use strict";l.querySelector&&d.addEventListener&&"undefined"!=typeof URL&&(d.wp=d.wp||{},d.wp.receiveEmbedMessage||(d.wp.receiveEmbedMessage=function(e){var t=e.data;if((t||t.secret||t.message||t.value)&&!/[^a-zA-Z0-9]/.test(t.secret)){for(var s,r,n,a=l.querySelectorAll('iframe[data-secret="'+t.secret+'"]'),o=l.querySelectorAll('blockquote[data-secret="'+t.secret+'"]'),c=new RegExp("^https?:$","i"),i=0;i<o.length;i++)o[i].style.display="none";for(i=0;i<a.length;i++)s=a[i],e.source===s.contentWindow&&(s.removeAttribute("style"),"height"===t.message?(1e3<(r=parseInt(t.value,10))?r=1e3:~~r<200&&(r=200),s.height=r):"link"===t.message&&(r=new URL(s.getAttribute("src")),n=new URL(t.value),c.test(n.protocol))&&n.host===r.host&&l.activeElement===s&&(d.top.location.href=t.value))}},d.addEventListener("message",d.wp.receiveEmbedMessage,!1),l.addEventListener("DOMContentLoaded",function(){for(var e,t,s=l.querySelectorAll("iframe.wp-embedded-content"),r=0;r<s.length;r++)(t=(e=s[r]).getAttribute("data-secret"))||(t=Math.random().toString(36).substring(2,12),e.src+="#?secret="+t,e.setAttribute("data-secret",t)),e.contentWindow.postMessage({message:"ready",secret:t},"*")},!1)))}(window,document); //# sourceURL=https://www.microsoft.com/en-us/research/wp-includes/js/wp-embed.min.js /* ]]> */ </script> Computer scientists have long believed that software is different from physical systems in one fundamental way: while the latter have continuous dynamics, the former do not. In this paper, we argue that notions of continuity from mathematical analysis are relevant and interesting even for software. First, we demonstrate that many everyday programs are continuous (i.e., […]