{"id":2873,"date":"2025-06-04T15:56:06","date_gmt":"2025-06-04T15:56:06","guid":{"rendered":"https:\/\/diznr.com\/?p=2873"},"modified":"2025-06-04T15:56:06","modified_gmt":"2025-06-04T15:56:06","slug":"gate-1990-subject-theory-of-computation-topic-finite-automata","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/gate-1990-subject-theory-of-computation-topic-finite-automata\/","title":{"rendered":"GATE 1990 Subject &#8211; Theory Of Computation Topic -Finite Automata."},"content":{"rendered":"<p>GATE 1990 Subject &#8211; Theory Of Computation Topic -Finite Automata.<\/p>\n<p>[fvplayer id=&#8221;153&#8243;]<\/p>\n<p>\u092c\u093f\u0932\u0915\u0941\u0932! \u0928\u0940\u091a\u0947 <strong>GATE 1990<\/strong> \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 <strong>Theory of Computation<\/strong> \u0935\u093f\u0937\u092f \u092e\u0947\u0902 \u0938\u0947 <strong>Finite Automata (FA)<\/strong> \u091f\u0949\u092a\u093f\u0915 \u0915\u093e \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u090f\u0915 \u0938\u094d\u092a\u0937\u094d\u091f \u0914\u0930 \u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0938\u093e\u0930\u093e\u0902\u0936 \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u091c\u094b \u0924\u0948\u092f\u093e\u0930\u0940 \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930\u0947\u0917\u093e\u0964<\/p>\n<hr \/>\n<h2>\ud83d\udcd8 <strong>GATE 1990 \u2013 Theory of Computation<\/strong><\/h2>\n<h3>\ud83d\udd39 <strong>\u0935\u093f\u0937\u092f (Topic)<\/strong>: Finite Automata (FA)<\/h3>\n<p><strong>\u092d\u093e\u0937\u093e<\/strong>: \u0939\u093f\u0902\u0926\u0940<\/p>\n<hr \/>\n<h2>\ud83d\udd0d <strong>Finite Automata \u0915\u094d\u092f\u093e \u0939\u0948?<\/strong><\/h2>\n<p><strong>Finite Automaton (FA)<\/strong> \u090f\u0915 \u0917\u0923\u0928\u093e\u0924\u094d\u092e\u0915 \u092e\u0949\u0921\u0932 \u0939\u0948, \u091c\u094b \u0907\u0928\u092a\u0941\u091f \u0938\u094d\u091f\u094d\u0930\u093f\u0902\u0917 \u0915\u094b \u092a\u0922\u093c\u0915\u0930 \u092f\u0939 \u0924\u092f \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f \u0935\u0939 \u0915\u093f\u0938\u0940 <strong>language<\/strong> \u0915\u093e \u0939\u093f\u0938\u094d\u0938\u093e \u0939\u0948 \u092f\u093e \u0928\u0939\u0940\u0902\u0964 \u092f\u0939 \u0938\u0940\u092e\u093f\u0924 \u0938\u0902\u0916\u094d\u092f\u093e \u092e\u0947\u0902 \u0938\u094d\u091f\u0947\u091f\u094d\u0938 \u0915\u0947 \u0938\u093e\u0925 \u0915\u093e\u092e \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/p>\n<hr \/>\n<h2>\u2728 <strong>\u092e\u0941\u0916\u094d\u092f \u092a\u094d\u0930\u0915\u093e\u0930 (Types of FA)<\/strong><\/h2>\n<table>\n<thead>\n<tr>\n<th>\u092a\u094d\u0930\u0915\u093e\u0930<\/th>\n<th>\u0928\u093e\u092e<\/th>\n<th>\u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0930\u0942\u092a<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>1\ufe0f\u20e3<\/td>\n<td>Deterministic Finite Automaton<\/td>\n<td>DFA<\/td>\n<\/tr>\n<tr>\n<td>2\ufe0f\u20e3<\/td>\n<td>Non-Deterministic Finite Automaton<\/td>\n<td>NFA<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h3>\u2705 <strong>1. Deterministic Finite Automaton (DFA)<\/strong><\/h3>\n<ul>\n<li>\u0939\u0930 \u0907\u0928\u092a\u0941\u091f \u0914\u0930 \u0939\u0930 \u0938\u094d\u091f\u0947\u091f \u092a\u0930 <strong>\u0938\u093f\u0930\u094d\u092b \u090f\u0915 \u091f\u094d\u0930\u093e\u0902\u091c\u093c\u093f\u0936\u0928<\/strong> \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/li>\n<li>\u0915\u094b\u0908 \u0905\u0928\u093f\u0936\u094d\u091a\u093f\u0924\u0924\u093e \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u0940\u0964<\/li>\n<\/ul>\n<p>\ud83d\udccc <strong>Definition (DFA):<\/strong><br \/>\nA DFA is a 5-tuple (Q, \u03a3, \u03b4, q\u2080, F), where:<\/p>\n<ul>\n<li>Q = Finite set of states<\/li>\n<li>\u03a3 = Input alphabet<\/li>\n<li>\u03b4 = Transition function (\u03b4: Q \u00d7 \u03a3 \u2192 Q)<\/li>\n<li>q\u2080 = Start state<\/li>\n<li>F = Set of final\/accepting states<\/li>\n<\/ul>\n<hr \/>\n<h3>\u2705 <strong>2. Non-Deterministic Finite Automaton (NFA)<\/strong><\/h3>\n<ul>\n<li>\u090f\u0915 \u0907\u0928\u092a\u0941\u091f \u092a\u0930 <strong>\u090f\u0915 \u0938\u0947 \u0905\u0927\u093f\u0915<\/strong> \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u091f\u094d\u0930\u093e\u0902\u091c\u093c\u093f\u0936\u0928 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/li>\n<li>\u0915\u092d\u0940-\u0915\u092d\u0940 <strong>\u03b5 (epsilon)<\/strong> \u091f\u094d\u0930\u093e\u0902\u091c\u093c\u093f\u0936\u0928 \u092d\u0940 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964<\/li>\n<\/ul>\n<p>\ud83d\udccc <strong>NFA \u092e\u0947\u0902 Acceptance:<\/strong><br \/>\n\u0905\u0917\u0930 \u0915\u094b\u0908 \u090f\u0915 \u092d\u0940 path accepting state \u0924\u0915 \u092a\u0939\u0941\u0902\u091a \u091c\u093e\u090f, \u0924\u094b input \u0938\u094d\u0935\u0940\u0915\u093e\u0930 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<hr \/>\n<h2>\u2699\ufe0f <strong>DFA \u0914\u0930 NFA \u092e\u0947\u0902 \u0905\u0902\u0924\u0930 (Differences):<\/strong><\/h2>\n<table>\n<thead>\n<tr>\n<th>\u0935\u093f\u0936\u0947\u0937\u0924\u093e<\/th>\n<th>DFA<\/th>\n<th>NFA<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Determinism<\/td>\n<td>\u0939\u093e\u0901<\/td>\n<td>\u0928\u0939\u0940\u0902<\/td>\n<\/tr>\n<tr>\n<td>\u091f\u094d\u0930\u093e\u0902\u091c\u093c\u093f\u0936\u0928<\/td>\n<td>\u090f\u0915 \u0939\u0940<\/td>\n<td>\u090f\u0915 \u0938\u0947 \u0905\u0927\u093f\u0915<\/td>\n<\/tr>\n<tr>\n<td>\u0938\u0930\u0932\u0924\u093e<\/td>\n<td>\u091c\u091f\u093f\u0932<\/td>\n<td>\u0906\u0938\u093e\u0928 \u0921\u093f\u091c\u093c\u093e\u0907\u0928<\/td>\n<\/tr>\n<tr>\n<td>Execution<\/td>\n<td>Fast<\/td>\n<td>Theoretical fast<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\ud83d\udca1 <em>\u0939\u0930 NFA \u0915\u093e \u090f\u0915 \u0938\u092e\u0915\u0915\u094d\u0937 DFA \u0939\u094b\u0924\u093e \u0939\u0948 (NFA \u21d2 DFA Conversion \u0938\u0902\u092d\u0935 \u0939\u0948)<\/em><\/p>\n<hr \/>\n<h2>\ud83e\udde0 <strong>GATE 1990 \u091c\u0948\u0938\u0947 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0938\u0941\u091d\u093e\u0935:<\/strong><\/h2>\n<h3>\ud83c\udfaf \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u094d\u0930\u0915\u093e\u0930:<\/h3>\n<ol>\n<li>\u0915\u093f\u0938\u0940 DFA\/NFA \u0915\u094b \u0926\u0947\u0916\u0915\u0930 \u092f\u0939 \u092c\u0924\u093e\u0928\u093e \u0915\u093f \u0915\u094c\u0928 \u0938\u0940 language \u090f\u0915\u094d\u0938\u0947\u092a\u094d\u091f \u0939\u094b\u0924\u0940 \u0939\u0948\u0964<\/li>\n<li>NFA \u0915\u094b DFA \u092e\u0947\u0902 \u092c\u0926\u0932\u0928\u093e\u0964<\/li>\n<li>Regular Expression \u0938\u0947 FA \u092c\u0928\u093e\u0928\u093e\u0964<\/li>\n<li>Language \u0915\u0940 \u092a\u0939\u091a\u093e\u0928: finite\/infinite, regular\/non-regular\u0964<\/li>\n<\/ol>\n<hr \/>\n<h3>\ud83d\udccc <strong>\u0909\u0926\u093e\u0939\u0930\u0923 (Example DFA):<\/strong><\/h3>\n<p>\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f, \u0939\u092e\u0947\u0902 \u0909\u0938 language \u0915\u093e DFA \u092c\u0928\u093e\u0928\u093e \u0939\u0948 \u091c\u094b <strong>\u0938\u093f\u0930\u094d\u092b even number of 1s<\/strong> \u0915\u094b \u090f\u0915\u094d\u0938\u0947\u092a\u094d\u091f \u0915\u0930\u0924\u0940 \u0939\u0948:<\/p>\n<p><strong>States:<\/strong><\/p>\n<ul>\n<li>q0: Even number of 1s<\/li>\n<li>q1: Odd number of 1s<\/li>\n<\/ul>\n<p><strong>Transition Table:<\/strong><\/p>\n<table>\n<thead>\n<tr>\n<th>State<\/th>\n<th>Input 0<\/th>\n<th>Input 1<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>q0<\/td>\n<td>q0<\/td>\n<td>q1<\/td>\n<\/tr>\n<tr>\n<td>q1<\/td>\n<td>q1<\/td>\n<td>q0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Start state = q0<br \/>\nAccepting state = q0<\/p>\n<hr \/>\n<h2>\ud83d\udcda <strong>Final Tips for GATE:<\/strong><\/h2>\n<ul>\n<li><strong>DFA\/NFA \u0915\u0947 diagrams<\/strong> \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u0914\u0930 \u092c\u0928\u093e\u0928\u0947 \u0915\u0940 \u092a\u094d\u0930\u0948\u0915\u094d\u091f\u093f\u0938 \u0915\u0930\u0947\u0902\u0964<\/li>\n<li>Regular expressions \u0938\u0947 FA \u092c\u0928\u093e\u0928\u093e \u0938\u0940\u0916\u0947\u0902\u0964<\/li>\n<li><strong>Closure properties, language equivalence, \u0914\u0930 minimization<\/strong> \u0905\u091a\u094d\u091b\u0947 \u0938\u0947 \u092a\u0922\u093c\u0947\u0902\u0964<\/li>\n<\/ul>\n<hr \/>\n<p>\u0915\u094d\u092f\u093e \u0906\u092a \u091a\u093e\u0939\u0947\u0902\u0917\u0947 \u0915\u093f \u092e\u0948\u0902 \u0906\u092a\u0915\u094b GATE 1990 \u0915\u093e <strong>original MCQ question on FA<\/strong> \u092f\u093e \u0909\u0938\u0915\u093e <strong>practice test<\/strong> \u092d\u0940 \u0926\u0942\u0902?<\/p>\n<h3><a href=\"https:\/\/www.hnbgu.ac.in\/sites\/default\/files\/2021-08\/Syllabus%20M.Sc_.%20%28IT%29%20Programme.pdf\" target=\"_blank\" rel=\"noopener\">GATE 1990 Subject &#8211; Theory Of Computation Topic -Finite Automata.<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/apps.dtic.mil\/sti\/tr\/pdf\/ADA229432.pdf\" target=\"_blank\" rel=\"noopener\">A Complexity Theory of Neural Networks &#8211; DTIC<\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"<p>GATE 1990 Subject &#8211; Theory Of Computation Topic -Finite Automata. [fvplayer id=&#8221;153&#8243;] \u092c\u093f\u0932\u0915\u0941\u0932! \u0928\u0940\u091a\u0947 GATE 1990 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 Theory of Computation \u0935\u093f\u0937\u092f \u092e\u0947\u0902 \u0938\u0947 Finite Automata (FA) \u091f\u0949\u092a\u093f\u0915 \u0915\u093e \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u090f\u0915 \u0938\u094d\u092a\u0937\u094d\u091f \u0914\u0930 \u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0938\u093e\u0930\u093e\u0902\u0936 \u0926\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u091c\u094b \u0924\u0948\u092f\u093e\u0930\u0940 \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930\u0947\u0917\u093e\u0964 \ud83d\udcd8 GATE 1990 \u2013 Theory of Computation \ud83d\udd39 \u0935\u093f\u0937\u092f (Topic): Finite [&hellip;]<\/p>\n","protected":false},"author":71,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1310],"tags":[],"class_list":["post-2873","post","type-post","status-publish","format-standard","hentry","category-theory-of-computation"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2873","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/users\/71"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/comments?post=2873"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2873\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=2873"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=2873"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=2873"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}