{"id":10390,"date":"2020-10-30T11:09:31","date_gmt":"2020-10-30T10:09:31","guid":{"rendered":"https:\/\/complex-systems-ai.com\/?page_id=10390"},"modified":"2022-12-03T23:05:05","modified_gmt":"2022-12-03T22:05:05","slug":"projet-chaines-de-markov-computer-chess","status":"publish","type":"page","link":"https:\/\/complex-systems-ai.com\/en\/markov-process\/project-chains-of-markov-computer-chess\/","title":{"rendered":"Markov Chains Project: Computer Chess"},"content":{"rendered":"<div data-elementor-type=\"wp-page\" data-elementor-id=\"10390\" class=\"elementor elementor-10390\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-314a7a6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"314a7a6\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-078f34b\" data-id=\"078f34b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8d3db21 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"8d3db21\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/en\/2020\/04\/03\/theories-and-algorithms-2\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Theories<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-cc770b5\" data-id=\"cc770b5\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e6474c2 elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"e6474c2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/complex-systems-ai.com\/en\/\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Home page<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-b5e2f61\" data-id=\"b5e2f61\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-245419a elementor-align-justify elementor-widget elementor-widget-button\" data-id=\"245419a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm\" href=\"https:\/\/www.youtube.com\/watch?v=dQw4w9WgXcQ\" target=\"_blank\" rel=\"noopener\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t\t\t\t<span class=\"elementor-button-text\">Solution<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5c7d73d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5c7d73d\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-dd19f3d\" data-id=\"dd19f3d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-59f5819 elementor-widget elementor-widget-heading\" data-id=\"59f5819\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_82_2 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewbox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewbox=\"0 0 24 24\" version=\"1.2\" baseprofile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/complex-systems-ai.com\/en\/markov-process\/project-chains-of-markov-computer-chess\/#Projet-chaines-de-Markov-Computer-Chess\" >Markov Chains Project: Computer Chess<\/a><ul class='ez-toc-list-level-3' ><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/complex-systems-ai.com\/en\/markov-process\/project-chains-of-markov-computer-chess\/#%E2%80%9CCameraman-Do-you-think-a-human-being-will-ever-beat-a-person-at-chess-John-Oh-between-a-human-being-and-a-person-My-moneys-on-the-computer%E2%80%9D\" >\u201cCameraman: Do you think a human being will ever beat a person at chess? John: Oh ... between a human being and a person? My money&#039;s on the computer. \u201d<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/complex-systems-ai.com\/en\/markov-process\/project-chains-of-markov-computer-chess\/#Partie-1-Des-donnees-lisibles-et-comprehensibles\" >Part 1: Readable and understandable data<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/complex-systems-ai.com\/en\/markov-process\/project-chains-of-markov-computer-chess\/#Notation\" >Rating<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/complex-systems-ai.com\/en\/markov-process\/project-chains-of-markov-computer-chess\/#Partie-2-Etude-du-comportement\" >Part 2: Behavior study<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/complex-systems-ai.com\/en\/markov-process\/project-chains-of-markov-computer-chess\/#Notation-2\" >Rating<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/complex-systems-ai.com\/en\/markov-process\/project-chains-of-markov-computer-chess\/#Partie-3-Reduction-de-lautomate-et-prediction\" >Part 3: Automaton reduction and prediction<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/complex-systems-ai.com\/en\/markov-process\/project-chains-of-markov-computer-chess\/#Notation-3\" >Rating<\/a><\/li><\/ul><\/nav><\/div>\n<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Projet-chaines-de-Markov-Computer-Chess\"><\/span>Markov Chains Project: Computer Chess<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8f537dd elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8f537dd\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-383fb00\" data-id=\"383fb00\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8a9e251 elementor-widget elementor-widget-text-editor\" data-id=\"8a9e251\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The Markov chains project: Computer Chess, brings together notions of <a href=\"https:\/\/complex-systems-ai.com\/en\/language-theory\/\">language theory<\/a> and first-order discrete stochastic processes.<\/p><p>ETC: 15 hours (deadline - 5 classes)<\/p><p>2-3 students per team<\/p><p>Please take your time on both quality and contents<\/p><p>Associate professor and assistant professors will not answer questions about the project.<\/p><p><strong><u><b>SCALE: 40 points<\/b><\/u><\/strong><\/p><ol><li><u>10 Points<\/u><\/li><li><u>15 Points<\/u><\/li><li><u>15 points<\/u><\/li><\/ol><p><img decoding=\"async\" class=\"aligncenter wp-image-8945 size-full\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/09\/Capture.png\" alt=\"The Markov Chains Project: Computer Chess, brings together notions of language theory and discrete stochastic processes of order one\" width=\"97\" height=\"98\" title=\"\"><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2a31ba5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2a31ba5\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d4b4fa3\" data-id=\"d4b4fa3\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7d7f003 elementor-widget elementor-widget-image\" data-id=\"7d7f003\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"1024\" height=\"768\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image6-1024x768.png\" class=\"attachment-large size-large wp-image-10395\" alt=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image6-1024x768.png 1024w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image6-300x225.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image6-768x576.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image6-1000x750.png 1000w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image6.png 1066w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" title=\"\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-fc9f5f8 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fc9f5f8\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f733096\" data-id=\"f733096\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-32d1fa9 elementor-widget elementor-widget-heading\" data-id=\"32d1fa9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"%E2%80%9CCameraman-Do-you-think-a-human-being-will-ever-beat-a-person-at-chess-John-Oh-between-a-human-being-and-a-person-My-moneys-on-the-computer%E2%80%9D\"><\/span>\u201cCameraman: Do you think a human being will ever beat a person at chess? John: Oh ... between a human being and a person? My money&#039;s on the computer. \u201d<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ea5c0d3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ea5c0d3\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4b9890e\" data-id=\"4b9890e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-027eecf elementor-widget-divider--separator-type-pattern elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"027eecf\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\" style=\"--divider-pattern-url: url(&quot;data:image\/svg+xml,%3Csvg xmlns=&#039;http:\/\/www.w3.org\/2000\/svg&#039; preserveAspectRatio=&#039;none&#039; overflow=&#039;visible&#039; height=&#039;100%&#039; viewBox=&#039;0 0 24 24&#039; fill=&#039;none&#039; stroke=&#039;black&#039; stroke-width=&#039;1&#039; stroke-linecap=&#039;square&#039; stroke-miterlimit=&#039;10&#039;%3E%3Cpolyline points=&#039;0,18 12,6 24,18 &#039;\/%3E%3C\/svg%3E&quot;);\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-49d0392 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"49d0392\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-cb5f7e0\" data-id=\"cb5f7e0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7c69207 elementor-widget elementor-widget-heading\" data-id=\"7c69207\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Partie-1-Des-donnees-lisibles-et-comprehensibles\"><\/span>Part 1: Readable and understandable data<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b4f5eb1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b4f5eb1\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-fff258e\" data-id=\"fff258e\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b9c0178 elementor-widget elementor-widget-image\" data-id=\"b9c0178\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1024\" height=\"575\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image7-1024x575.png\" class=\"attachment-large size-large wp-image-10396\" alt=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image7-1024x575.png 1024w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image7-300x169.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image7-768x432.png 768w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image7-1000x562.png 1000w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image7.png 1050w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" title=\"\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a6b01a1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a6b01a1\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-e7715b0\" data-id=\"e7715b0\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3923f63 elementor-widget elementor-widget-text-editor\" data-id=\"3923f63\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em><i>&quot; TO\u00a0<\/i><\/em><em><i>computer<\/i><\/em><em><i>\u00a0once beat me at\u00a0<\/i><\/em><em><i>chess<\/i><\/em><em><i>, but it was no match for me at kick boxing. &quot;<\/i><\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d3d7b35 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d3d7b35\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b716f15\" data-id=\"b716f15\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a78cdb9 elementor-widget elementor-widget-text-editor\" data-id=\"a78cdb9\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>The challenge is tall, the annual global chess tournament to challenge the early computer scientists: to create a program capable of beating a human at chess. This is a first, and you have to show the world the potential of IT.<\/p><p>In order to familiarize yourself with the rules of chess, you watch in a loop the old tournaments of Mikhail Tal, Bobby Fisher and Anatoly Karpov as well as the promising debut of the young and formidable Garry Kasparov.<\/p><p>Possible moves (in terms of movement, not position) are recorded as symbols of the alphabet. A series of decision-making moves means that from a given favorable configuration, there is at least one strategy allowing to surely reach a favorable position of checkmate.<\/p><p>The computer will therefore build decision trees for favorable configurations (as in project 1). Take for example the following words for a favorable configuration A:<\/p><ul><li>abbaaccad<\/li><li>baacdaadd<\/li><li>abaacdddd<\/li><\/ul><p>In order to reduce the tree, we are going to use another technique than for subject 1. In the first step, you will assign in addition to the symbol, the number of times the arc has passed. Initially this number is equal to 1 for each arc.<\/p><p>The second step consists in calculating the coefficient of compatibility between two states. In our example we will merge two states if they are 100% compatible. Two states are 100% compatible if they have the same predecessor and successor symbols. For example on the prefixes abba and baab, the binomial ab or ba are 100% compatible. During the merger, it is also necessary to merge the number of passages through the arcs (so here we sum 1 + 1).<\/p><p>The third step is to merge compatible 50% states, that is to say with only the same successors or only the same predecessors. It is therefore possible to converge the final states into a single final state, since all the final states have the same successors (here the empty set).<\/p><p>The fourth and last step is used to manufacture the Markov chain in associated discrete time. For each state, the probability of the entry (resp. Exit) arcs is equal to the number of passages of this arc divided by the sum of the numbers of entry (or exit, this number is the same).<\/p><h2><span class=\"ez-toc-section\" id=\"Notation\"><\/span><strong><b>Rating<\/b><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2><ol><li>Step 1 <strong><b>(2 points)<\/b><\/strong><\/li><li>2nd step <strong><b>(3 points)<\/b><\/strong><\/li><li>Step 3 - do not converge on all the possible cases, at least two of which the final state <strong><b>(3 points)<\/b><\/strong><\/li><li>Step 4 <strong><b>(2 points)<\/b><\/strong><\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-931cffc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"931cffc\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-dab14e9\" data-id=\"dab14e9\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-1abd54a elementor-widget-divider--separator-type-pattern elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"1abd54a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\" style=\"--divider-pattern-url: url(&quot;data:image\/svg+xml,%3Csvg xmlns=&#039;http:\/\/www.w3.org\/2000\/svg&#039; preserveAspectRatio=&#039;none&#039; overflow=&#039;visible&#039; height=&#039;100%&#039; viewBox=&#039;0 0 24 24&#039; fill=&#039;none&#039; stroke=&#039;black&#039; stroke-width=&#039;1&#039; stroke-linecap=&#039;square&#039; stroke-miterlimit=&#039;10&#039;%3E%3Cpolyline points=&#039;0,18 12,6 24,18 &#039;\/%3E%3C\/svg%3E&quot;);\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6be248d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6be248d\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f469fed\" data-id=\"f469fed\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f729e2e elementor-widget elementor-widget-heading\" data-id=\"f729e2e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Partie-2-Etude-du-comportement\"><\/span>Part 2: Behavior study<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a9f3788 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a9f3788\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-fd8bd5c\" data-id=\"fd8bd5c\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-172e545 elementor-widget elementor-widget-image\" data-id=\"172e545\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"600\" height=\"450\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image8.png\" class=\"attachment-large size-large wp-image-10397\" alt=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image8.png 600w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image8-300x225.png 300w\" sizes=\"(max-width: 600px) 100vw, 600px\" title=\"\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6e8709b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6e8709b\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4d59f61\" data-id=\"4d59f61\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-09a9f7f elementor-widget elementor-widget-text-editor\" data-id=\"09a9f7f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em><i>&quot;\u00a0<\/i><\/em>Beuscher<em><i>: <\/i><\/em><em><i>Is there any possibility that this is uh\u2026 some kind of uh\u2026 very advanced\u2026 I mean, we just gave up a queen to get his queen and now we&#039;re basically just\u2026 um\u2026 \u201d<\/i><\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a0d8319 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a0d8319\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-9fe2675\" data-id=\"9fe2675\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-30926dd elementor-widget elementor-widget-text-editor\" data-id=\"30926dd\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Now that you have stochastic automata (a delicious mix of automaton and <a href=\"https:\/\/complex-systems-ai.com\/en\/markov-process\/discrete-time-markov-chains\/\">markov chain<\/a>), it is time to study their behavior, that is, the study of the associated Markov chain. Remember to carefully analyze the final states (checkmate).<\/p><p>Study the behavior of the following two discrete-time Markov chains:<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-10398\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image9-300x130.png\" alt=\"\" width=\"300\" height=\"130\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image9-300x130.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image9.png 341w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p><p>State 6 is a final state.<\/p><p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-medium wp-image-10399\" src=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image10-300x119.png\" alt=\"\" width=\"300\" height=\"119\" title=\"\" srcset=\"https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image10-300x119.png 300w, https:\/\/complex-systems-ai.com\/wp-content\/uploads\/2020\/10\/Image10.png 512w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/><\/p><p>The absorbing states are the \u201ccheckmate\u201d configurations. The state s0 is the initial state, the initial vector therefore begins only with this state.<\/p><h2><span class=\"ez-toc-section\" id=\"Notation-2\"><\/span><strong><b>Rating<\/b><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2><ol><li>Channel 1 <strong><b>(7 points)<\/b><\/strong><\/li><li>Channel 2 <strong><b>(8 points)<\/b><\/strong><strong><b><br \/><\/b><\/strong><\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-31b20e3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"31b20e3\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-694fd1a\" data-id=\"694fd1a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-50cbd3c elementor-widget-divider--separator-type-pattern elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"50cbd3c\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\" style=\"--divider-pattern-url: url(&quot;data:image\/svg+xml,%3Csvg xmlns=&#039;http:\/\/www.w3.org\/2000\/svg&#039; preserveAspectRatio=&#039;none&#039; overflow=&#039;visible&#039; height=&#039;100%&#039; viewBox=&#039;0 0 24 24&#039; fill=&#039;none&#039; stroke=&#039;black&#039; stroke-width=&#039;1&#039; stroke-linecap=&#039;square&#039; stroke-miterlimit=&#039;10&#039;%3E%3Cpolyline points=&#039;0,18 12,6 24,18 &#039;\/%3E%3C\/svg%3E&quot;);\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-b5606e2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b5606e2\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4604927\" data-id=\"4604927\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8552621 elementor-widget elementor-widget-heading\" data-id=\"8552621\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\"><span class=\"ez-toc-section\" id=\"Partie-3-Reduction-de-lautomate-et-prediction\"><\/span>Part 3: Automaton reduction and prediction<span class=\"ez-toc-section-end\"><\/span><\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-fc41dc6 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fc41dc6\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7134688\" data-id=\"7134688\" 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title=\"\">\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1c4caff elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1c4caff\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c50b996\" data-id=\"c50b996\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a87e6a3 elementor-widget elementor-widget-text-editor\" data-id=\"a87e6a3\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><em><i>\u201cChess is the struggle against the error.\u201d - <\/i><\/em><em><i>Johannes zukertort <\/i><\/em><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1e68ad2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1e68ad2\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a05526b\" data-id=\"a05526b\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-32c2e80 elementor-widget elementor-widget-text-editor\" data-id=\"32c2e80\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>Now that your machine learning system is up and running, it&#039;s time to think about the technical part. Your computer has two Cores and thus it is possible to do parallel computing. The Bus problem then arises, do you need one Bus or two Buses to route the information to the processors? Knowing that information always arrives according to a <a href=\"https:\/\/complex-systems-ai.com\/en\/markov-process\/fish-process\/\">Poisson process<\/a> of rate \u03bb and that they are served with a Poisson process of similar rate, calculate the stationary distribution, the occupation of the processors, the number of messages lost as well as the average waiting time before being served for both setups.<\/p><h2><span class=\"ez-toc-section\" id=\"Notation-3\"><\/span><strong><b>Rating<\/b><\/strong><span class=\"ez-toc-section-end\"><\/span><\/h2><ol><li>Modeling of the two configurations <strong><b>(5 points)<\/b><\/strong><\/li><li>Analysis of the first configuration <strong><b>(5 points)<\/b><\/strong><\/li><li>Analysis of the second configuration <strong><b>(5 points)<\/b><\/strong><\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>","protected":false},"excerpt":{"rendered":"<p>Theories Home Solution Markov Chains Project: Computer Chess The Markov Chains Project: Computer Chess brings together notions of theory of \u2026 <\/p>","protected":false},"author":1,"featured_media":0,"parent":5007,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"elementor_header_footer","meta":{"footnotes":""},"class_list":["post-10390","page","type-page","status-publish","hentry"],"amp_enabled":false,"_links":{"self":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/10390","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/comments?post=10390"}],"version-history":[{"count":7,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/10390\/revisions"}],"predecessor-version":[{"id":19034,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/10390\/revisions\/19034"}],"up":[{"embeddable":true,"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/pages\/5007"}],"wp:attachment":[{"href":"https:\/\/complex-systems-ai.com\/en\/wp-json\/wp\/v2\/media?parent=10390"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}