{"id":7712,"date":"2013-08-21T15:55:25","date_gmt":"2013-08-21T20:55:25","guid":{"rendered":"http:\/\/mjtsai.com\/blog\/?p=7712"},"modified":"2013-08-21T15:55:25","modified_gmt":"2013-08-21T20:55:25","slug":"i-hate-the-pumping-lemma","status":"publish","type":"post","link":"https:\/\/mjtsai.com\/blog\/2013\/08\/21\/i-hate-the-pumping-lemma\/","title":{"rendered":"The Pumping Lemma, The Pigeonhole Principle, and Differentiating Languages"},"content":{"rendered":"<p><a href=\"http:\/\/bosker.wordpress.com\/2013\/08\/18\/i-hate-the-pumping-lemma\/\">Robin Houston<\/a> (via <a href=\"https:\/\/twitter.com\/CompSciFact\/status\/369442167363600386\">@CompSciFact<\/a>):<\/p>\n<blockquote cite=\"http:\/\/bosker.wordpress.com\/2013\/08\/18\/i-hate-the-pumping-lemma\/\">\n<p>I hate the Pumping Lemma for regular languages. It&rsquo;s a complicated way to express an idea that is fundamentally very simple, and it isn&rsquo;t even a very good way to prove that a language is not regular.<\/p>\n<p>[&#8230;]<\/p>\n<p>It&rsquo;s easy enough to see that any derivative of a regular language is again regular: taking a derivative just corresponds to changing the start state in a deterministic automaton. By the same argument, any regular language has only a finite number of different derivatives.<\/p><\/blockquote>","protected":false},"excerpt":{"rendered":"<p>Robin Houston (via @CompSciFact): I hate the Pumping Lemma for regular languages. It&rsquo;s a complicated way to express an idea that is fundamentally very simple, and it isn&rsquo;t even a very good way to prove that a language is not regular. [&#8230;] It&rsquo;s easy enough to see that any derivative of a regular language is [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"apple_news_api_created_at":"","apple_news_api_id":"","apple_news_api_modified_at":"","apple_news_api_revision":"","apple_news_api_share_url":"","apple_news_coverimage":0,"apple_news_coverimage_caption":"","apple_news_is_hidden":false,"apple_news_is_paid":false,"apple_news_is_preview":false,"apple_news_is_sponsored":false,"apple_news_maturity_rating":"","apple_news_metadata":"\"\"","apple_news_pullquote":"","apple_news_pullquote_position":"","apple_news_slug":"","apple_news_sections":"\"\"","apple_news_suppress_video_url":false,"apple_news_use_image_component":false,"footnotes":""},"categories":[2],"tags":[263,234],"class_list":["post-7712","post","type-post","status-publish","format-standard","hentry","category-technology","tag-theory","tag-regex"],"apple_news_notices":[],"_links":{"self":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/posts\/7712","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/comments?post=7712"}],"version-history":[{"count":0,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/posts\/7712\/revisions"}],"wp:attachment":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/media?parent=7712"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/categories?post=7712"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/tags?post=7712"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}