{"id":42,"date":"2015-04-09T13:19:14","date_gmt":"2015-04-09T11:19:14","guid":{"rendered":"http:\/\/localhost\/web\/podpunkt2\/?page_id=42"},"modified":"2016-05-18T17:16:50","modified_gmt":"2016-05-18T15:16:50","slug":"alg","status":"publish","type":"page","link":"https:\/\/www.mimuw.edu.pl\/~bojan\/20142015-2\/alg","title":{"rendered":"Algebraic Language Theory"},"content":{"rendered":"<p>This course is about an alternative approach to regular languages, where one uses monoids or semigroups instead of automata.<\/p>\n<p><strong>Lecture<\/strong>: Tuesdays 8:45-10:15 (room 5070)<br \/>\n<strong>Exercises<\/strong>: Tuesdays 10:25-11:55 (room 5070)<\/p>\n<p><!--more--><\/p>\n<p><strong>Exam<br \/>\n<\/strong><\/p>\n<p>There will be an oral exam. The grade can be improved by doing special assignments, which will appear throughout the semester.<\/p>\n<p><strong>Plan\u00a0of the course<\/strong><\/p>\n<p><em>Finite words<\/em><\/p>\n<ul>\n<li><a title=\"1. Introduction to monoids\" href=\"http:\/\/duch.mimuw.edu.pl\/~bojan\/20142015-2\/alg\/1-introduction-to-monoids\">Recognising languages using monoids instead of automata<\/a><\/li>\n<li><a title=\"2. Green\u2019s relations\" href=\"http:\/\/duch.mimuw.edu.pl\/~bojan\/20142015-2\/alg\/2-greens-relations\">Green&#8217;s relations<\/a><\/li>\n<li><a title=\"3. The Sch\u00fctzenberger Theorem\" href=\"http:\/\/duch.mimuw.edu.pl\/~bojan\/20142015-2\/alg\/3-the-schutzenberger-theorem\">First-order logic equals aperiodic monoids<\/a><\/li>\n<li><a title=\"4. Factorisation trees\" href=\"http:\/\/duch.mimuw.edu.pl\/~bojan\/20142015-2\/alg\/4-factorisation-trees\">The factorisation forest theorem<\/a><\/li>\n<li><a title=\"5. Piecewise testable languages\" href=\"http:\/\/duch.mimuw.edu.pl\/~bojan\/20142015-2\/alg\/5-piecewise-testable-languages\">Piecewise testable languages<\/a><\/li>\n<\/ul>\n<p><em>Infinite words<\/em><\/p>\n<ul>\n<li><a title=\"6. B\u00fcchi automata\" href=\"http:\/\/duch.mimuw.edu.pl\/~bojan\/20142015-2\/alg\/6-buchi-automata\">Automata for\u00a0\u03c9-words<\/a><\/li>\n<li><a title=\"7. Algebra for infinite words\" href=\"http:\/\/duch.mimuw.edu.pl\/~bojan\/20142015-2\/alg\/algebra-for-infinite-words\">Algebra for \u03c9-words<\/a><\/li>\n<li>An interlude: <a title=\"8. Monads\" href=\"http:\/\/duch.mimuw.edu.pl\/~bojan\/20142015-2\/alg\/8-monads\">monads<\/a><\/li>\n<li><a title=\"9. Countable scattered chains\" href=\"http:\/\/duch.mimuw.edu.pl\/~bojan\/20142015-2\/alg\/10-countable-well-founded-chains\">Scattered infinite words<\/a><\/li>\n<li><a title=\"10. All countable chains\" href=\"http:\/\/www.mimuw.edu.pl\/~bojan\/20142015-2\/alg\/all-countable-chains-a-new-proof\">All\u00a0countable linear orders<\/a><\/li>\n<\/ul>\n<p><em>Profinite words<\/em><\/p>\n<ul>\n<li><a title=\"11. Profinite words\" href=\"http:\/\/duch.mimuw.edu.pl\/~bojan\/20142015-2\/alg\/11-profinite-words\">Profinite words<\/a><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>This course is about an alternative approach to regular languages, where one uses monoids or semigroups instead of automata. Lecture: Tuesdays 8:45-10:15 (room 5070) Exercises: Tuesdays 10:25-11:55 (room 5070)<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":40,"menu_order":1,"comment_status":"open","ping_status":"open","template":"","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"class_list":["post-42","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/pages\/42"}],"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=42"}],"version-history":[{"count":13,"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/pages\/42\/revisions"}],"predecessor-version":[{"id":1083,"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/pages\/42\/revisions\/1083"}],"up":[{"embeddable":true,"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/pages\/40"}],"wp:attachment":[{"href":"https:\/\/www.mimuw.edu.pl\/~bojan\/wp-json\/wp\/v2\/media?parent=42"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}