{"id":1328,"date":"2017-05-15T10:07:28","date_gmt":"2017-05-15T08:07:28","guid":{"rendered":"https:\/\/www.mimuw.edu.pl\/~bojan\/?page_id=1328"},"modified":"2018-01-17T12:17:45","modified_gmt":"2018-01-17T11:17:45","slug":"decision-problems-for-linear-recurrence-sequences","status":"publish","type":"page","link":"https:\/\/www.mimuw.edu.pl\/~bojan\/lipa\/lipa-summer-school\/decision-problems-for-linear-recurrence-sequences","title":{"rendered":"Decision Problems for Linear Recurrence Sequences"},"content":{"rendered":"<p>This one of the courses at the\u00a0<a href=\"https:\/\/www.mimuw.edu.pl\/~bojan\/lipa-summer-school\">Lipa Summer School<\/a>.<\/p>\n<h4>Jo\u00ebl Ouaknine<\/h4>\n<h4><em>Decision Problems for Linear Recurrence Sequences<\/em><\/h4>\n<p>Videos:\u00a0<a href=\"https:\/\/www.youtube.com\/watch?v=YhpJC6mwBHk\">1<\/a>,\u00a0<a href=\"https:\/\/www.youtube.com\/watch?v=GuBX_eEnhbw\">2<\/a>,\u00a0<a href=\"https:\/\/www.youtube.com\/watch?v=1STRX3DIi8I\">3<\/a>,\u00a0<a href=\"https:\/\/www.youtube.com\/watch?v=-XAMVw6pDEQ\">4<\/a><\/p>\n<p>Linear recurrence sequence (LRS), such as the Fibonacci numbers, permeate vast areas of mathematics, physics, and computer science. In this tutorial, I consider some fundamental decision problems for LRS over the integers, such as the Skolem Problem (does the sequence have a zero?) and the Positivity Problem (are all terms of the sequence positive?).<\/p>\n<div>\n<div>In general, the decidability of such problems is open, but various partial results are known. I will introduce some of the key mathematical tools for attacking these problems, and present some of the known results.<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>This one of the courses at the\u00a0Lipa Summer School. Jo\u00ebl Ouaknine Decision Problems for Linear Recurrence Sequences Videos:\u00a01,\u00a02,\u00a03,\u00a04 Linear recurrence sequence (LRS), such as the Fibonacci numbers, permeate vast areas of mathematics, physics, and computer science. In this tutorial, I consider some fundamental decision problems for LRS over the integers, such as the Skolem Problem [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":1283,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"class_list":["post-1328","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/pages\/1328"}],"collection":[{"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/comments?post=1328"}],"version-history":[{"count":7,"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/pages\/1328\/revisions"}],"predecessor-version":[{"id":1451,"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/pages\/1328\/revisions\/1451"}],"up":[{"embeddable":true,"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/pages\/1283"}],"wp:attachment":[{"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/media?parent=1328"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}