{"id":154008,"date":"2023-08-02T11:15:53","date_gmt":"2023-08-02T05:45:53","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=154008"},"modified":"2023-08-02T11:15:56","modified_gmt":"2023-08-02T05:45:56","slug":"if-%f0%9d%90%bf-is-a-regular-language-over-%cf%83-%f0%9d%91%8e-%f0%9d%91%8f-which-one-of-the-following-languages-is-not-regular","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/if-%f0%9d%90%bf-is-a-regular-language-over-%cf%83-%f0%9d%91%8e-%f0%9d%91%8f-which-one-of-the-following-languages-is-not-regular\/","title":{"rendered":"If \ud835\udc3f is a regular language over \u03a3 = {\ud835\udc4e, \ud835\udc4f}, which one of the following languages is NOT regular ?"},"content":{"rendered":"\n<p>Q. If \ud835\udc3f is a regular language over \u03a3 = {\ud835\udc4e, \ud835\udc4f}, which one of the following languages is NOT regular ?<\/p>\n\n\n\n<p>(A) \ud835\udc3f \u22c5 \ud835\udc3f<sup>\ud835\udc45<\/sup> = {\ud835\udc65\ud835\udc66 | \ud835\udc65 \u2208 \ud835\udc3f, \ud835\udc66<sup>\ud835\udc45<\/sup> \u2208 \ud835\udc3f}<\/p>\n\n\n\n<p>(B) {\ud835\udc64\ud835\udc64<sup>\ud835\udc45<\/sup> | \ud835\udc64 \u2208 \ud835\udc3f}<\/p>\n\n\n\n<p>(C) Prefix (\ud835\udc3f) = {\ud835\udc65 \u2208 \ud835\udef4<sup>\u2217<\/sup>|\u2203\ud835\udc66 \u2208 \ud835\udef4<sup>\u2217<\/sup> such that \ud835\udc65\ud835\udc66 \u2208 \ud835\udc3f}<\/p>\n\n\n\n<p>(D) Suffix (\ud835\udc3f) = {\ud835\udc66 \u2208 \ud835\udef4<sup>\u2217<\/sup>|\u2203\ud835\udc65 \u2208 \ud835\udef4<sup>\u2217<\/sup> such that \ud835\udc65\ud835\udc66 \u2208 \ud835\udc3f}<\/p>\n\n\n\n<p>Ans:{\ud835\udc64\ud835\udc64<sup>\ud835\udc45<\/sup> | \ud835\udc64 \u2208 \ud835\udc3f}<\/p>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<p>language L = {wwR \u23d0 w \u2208 L} is infinite and not regular because it involves string matching and we can increase in length indefinitely and then finite automata will run out of memory, so it require stack. Hence, it is context-free but not regular.<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. If \ud835\udc3f is a regular language over \u03a3 = {\ud835\udc4e, \ud835\udc4f}, which one of the following languages is NOT regular ? (A) \ud835\udc3f \u22c5 \ud835\udc3f\ud835\udc45 = {\ud835\udc65\ud835\udc66 | \ud835\udc65 \u2208 \ud835\udc3f, \ud835\udc66\ud835\udc45 \u2208 \ud835\udc3f} (B) {\ud835\udc64\ud835\udc64\ud835\udc45 | \ud835\udc64 \u2208 \ud835\udc3f} (C) Prefix (\ud835\udc3f) = {\ud835\udc65 \u2208 \ud835\udef4\u2217|\u2203\ud835\udc66 \u2208 \ud835\udef4\u2217 such that \ud835\udc65\ud835\udc66 \u2208 \ud835\udc3f} [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":154009,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[5141],"tags":[5140],"class_list":["post-154008","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154008","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=154008"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154008\/revisions"}],"predecessor-version":[{"id":154010,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154008\/revisions\/154010"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/154009"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=154008"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=154008"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=154008"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}