{"id":214899,"date":"2015-12-03T00:00:00","date_gmt":"2015-12-03T09:03:52","guid":{"rendered":"https:\/\/www.microsoft.com\/en-us\/research\/msr-research-item\/the-strange-logic-of-galton-watson-trees\/"},"modified":"2016-07-15T15:27:45","modified_gmt":"2016-07-15T22:27:45","slug":"the-strange-logic-of-galton-watson-trees","status":"publish","type":"msr-video","link":"https:\/\/www.microsoft.com\/en-us\/research\/video\/the-strange-logic-of-galton-watson-trees\/","title":{"rendered":"The Strange Logic of Galton-Watson Trees"},"content":{"rendered":"<div class=\"asset-content\">\n<p>The Galton-Watson tree is a basic demographic model. The classic equation for a Galton-Watson tree being infinite has two solutions, only one of which is &#8220;correct.&#8221; What about other properties. (Example: Some node has precisely two children.) We show that when the property is what is called first order than there is a unique solution to the corresponding equation. We consider &#8220;tree automata&#8221; and the situation for monadic second order properties.<\/p>\n<\/div>\n<p><!-- .asset-content --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Galton-Watson tree is a basic demographic model. The classic equation for a Galton-Watson tree being infinite has two solutions, only one of which is &#8220;correct.&#8221; What about other properties. (Example: Some node has precisely two children.) We show that when the property is what is called first order than there is a unique solution [&hellip;]<\/p>\n","protected":false},"featured_media":257367,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","footnotes":""},"research-area":[],"msr-video-type":[],"msr-locale":[268875],"msr-post-option":[],"msr-impact-theme":[],"msr-pillar":[],"class_list":["post-214899","msr-video","type-msr-video","status-publish","has-post-thumbnail","hentry","msr-locale-en_us"],"msr_download_urls":"","msr_external_url":"https:\/\/youtu.be\/C2USgy99hJY","msr_secondary_video_url":"","msr_video_file":"","_links":{"self":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/214899"}],"collection":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video"}],"about":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/types\/msr-video"}],"version-history":[{"count":0,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video\/214899\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media\/257367"}],"wp:attachment":[{"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/media?parent=214899"}],"wp:term":[{"taxonomy":"msr-research-area","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/research-area?post=214899"},{"taxonomy":"msr-video-type","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-video-type?post=214899"},{"taxonomy":"msr-locale","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-locale?post=214899"},{"taxonomy":"msr-post-option","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-post-option?post=214899"},{"taxonomy":"msr-impact-theme","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-impact-theme?post=214899"},{"taxonomy":"msr-pillar","embeddable":true,"href":"https:\/\/www.microsoft.com\/en-us\/research\/wp-json\/wp\/v2\/msr-pillar?post=214899"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}