1.0Microsoft Researchhttps://www.microsoft.com/en-us/researchJeff Runninghttps://www.microsoft.com/en-us/research/people/jeffrunn/rich600338<blockquote class="wp-embedded-content" data-secret="zdf4GxH7at"><a href="https://www.microsoft.com/en-us/research/video/mathematical-analysis-of-programs/">Mathematical Analysis of Programs</a></blockquote><iframe sandbox="allow-scripts" security="restricted" src="https://www.microsoft.com/en-us/research/video/mathematical-analysis-of-programs/embed/#?secret=zdf4GxH7at" width="600" height="338" title="“Mathematical Analysis of Programs” — Microsoft Research" data-secret="zdf4GxH7at" 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> https://www.microsoft.com/en-us/research/wp-content/uploads/2016/02/mathematical-analysis-of-programs-1.jpg320240Numerical programs are imperative programs over integer and real quantities. Such programs are ubiquitous. Common examples include scientific and systems programs, models of control systems such as timed and hybrid automata, and models of biological systems such as biochemical reaction mechanisms and gene regulatory networks. Static analyses of these programs automatically infer properties about the […]