{"id":1381,"date":"2017-10-02T15:59:32","date_gmt":"2017-10-02T13:59:32","guid":{"rendered":"https:\/\/www.mimuw.edu.pl\/~bojan\/?p=1381"},"modified":"2017-10-02T15:59:32","modified_gmt":"2017-10-02T13:59:32","slug":"hilberts-basis-theorem-and-transducers","status":"publish","type":"post","link":"https:\/\/www.mimuw.edu.pl\/~bojan\/posts\/hilberts-basis-theorem-and-transducers","title":{"rendered":"Hilbert&#8217;s Basis Theorem and transducers"},"content":{"rendered":"<p>These slides show how to decide equivalence of tree-to-string transducers using the Hilbert Basis Theorem. The idea is based on<\/p>\n<p>Helmut Seidl, Sebastian Maneth, Gregor Kemper:<br \/>\nEquivalence of Deterministic Top-Down Tree-to-String Transducers is Decidable. FOCS 2015: 943-962<\/p>\n<p>There are two parts:<\/p>\n<ol>\n<li>consider grammars that generate tuples of rational numbers, and use the Hilbert Basis Theorem to show that the following is decidable: &#8220;given a grammar, decide if the only tuple that it generates is the zero tuple&#8221;. <a href=\"https:\/\/www.mimuw.edu.pl\/~bojan\/slides\/Hilbert\/Hilbert.sozi.html#frame9687\">slides<\/a><\/li>\n<li>reduce the equivalence problem for transducers to the zero-ness problem discussed above. <a href=\"https:\/\/www.mimuw.edu.pl\/~bojan\/slides\/Hilbert\/Registers.sozi.html#frame5868\">slides<\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>These slides show how to decide equivalence of tree-to-string transducers using the Hilbert Basis Theorem. The idea is based on Helmut Seidl, Sebastian Maneth, Gregor Kemper: Equivalence of Deterministic Top-Down Tree-to-String Transducers is Decidable. FOCS 2015: 943-962 There are two parts: consider grammars that generate tuples of rational numbers, and use the Hilbert Basis Theorem [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[1],"tags":[],"class_list":["post-1381","post","type-post","status-publish","format-standard","hentry","category-posts"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/posts\/1381"}],"collection":[{"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/types\/post"}],"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=1381"}],"version-history":[{"count":1,"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/posts\/1381\/revisions"}],"predecessor-version":[{"id":1382,"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/posts\/1381\/revisions\/1382"}],"wp:attachment":[{"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/media?parent=1381"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/categories?post=1381"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/tags?post=1381"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}