GATE 1989 Subject – Theory Of Computation Topic -Finite Automata<\/p>\n
[fvplayer id=”154″]<\/p>\n
Here’s a focused breakdown of the GATE 1989<\/strong> paper, particularly for the Theory of Computation<\/strong> subject under the topic Finite Automata<\/strong>:<\/p>\n Before jumping into specific questions or examples from the 1989 paper, it\u2019s important to revise the following key concepts related to Finite Automata<\/strong>:<\/p>\n Deterministic Finite Automata (DFA)<\/strong><\/p>\n<\/li>\n Non-Deterministic Finite Automata (NFA)<\/strong><\/p>\n<\/li>\n Equivalence of DFA and NFA<\/strong><\/p>\n<\/li>\n Conversion: NFA to DFA<\/strong><\/p>\n<\/li>\n Minimization of DFA<\/strong><\/p>\n<\/li>\n Regular Languages and Regular Expressions<\/strong><\/p>\n<\/li>\n Language accepted by FA<\/strong><\/p>\n<\/li>\n Closure Properties of Regular Languages<\/strong><\/p>\n<\/li>\n Limitations of FA (e.g., not recognizing context-free languages)<\/strong><\/p>\n<\/li>\n<\/ol>\n Q1.<\/strong> a) Every NFA is also a DFA \u2705 Correct Answer: (b)<\/strong><\/p>\n Every DFA is also an NFA (a special case of NFA with exactly one transition per symbol per state). Q2.<\/strong> a) L is necessarily infinite \u2705 Correct Answer: (c)<\/strong><\/p>\n Any language accepted by a DFA is by definition a regular language<\/strong>.<\/p>\n<\/blockquote>\n Always draw a state diagram<\/strong> to better visualize transitions.<\/p>\n<\/li>\n Practice converting regular expressions<\/strong> to FA<\/strong> and vice versa.<\/p>\n<\/li>\n Be familiar with DFA minimization<\/strong> techniques (state equivalence method).<\/p>\n<\/li>\n Remember that every DFA is a unique NFA<\/strong>, but the reverse requires construction.<\/p>\n<\/li>\n<\/ul>\n Construct a DFA that accepts strings over Convert the given NFA to DFA.<\/p>\n<\/li>\n Minimize a given DFA and find its language.<\/p>\n<\/li>\n Given a regular expression, construct the equivalent NFA and DFA.<\/p>\n<\/li>\n<\/ol>\n Would you like the exact GATE 1989 question paper<\/strong> with solutions, or should I generate a custom practice test<\/strong> based on that year’s style and syllabus?<\/p>\n Certainly! Let’s delve into a specific question from the GATE 1989<\/strong> examination under the subject Theory of Computation<\/strong>, focusing on the topic of Finite Automata<\/strong>.<\/p>\n Question:<\/strong><\/p>\n Is the class of regular sets closed under infinite union? Explain.<\/em><\/p>\n Answer:<\/strong><\/p>\n The class of regular languages is not closed<\/strong> under infinite union.<\/span><\/p>\n Explanation:<\/strong><\/p>\n Regular languages are closed under operations such as union, intersection, and complement when applied finitely<\/strong>. However, when considering an infinite<\/strong> union of regular languages, the resulting language may not be regular.<\/span><\/p>\n Example:<\/strong><\/p>\n Consider the set of languages:<\/p>\n L\u2081 = { a }<\/span><\/p>\n<\/li>\n L\u2082 = { aa }<\/span><\/p>\n<\/li>\n L\u2083 = { aaa }<\/span><\/p>\n<\/li>\n …<\/p>\n<\/li>\n L\u2099 = { a\u207f }<\/span><\/p>\n<\/li>\n<\/ul>\n Each L\u2099 is regular. Now, consider the infinite union:<\/p>\n L = \u22c3\u2099\u208c\u2081^\u221e L\u2099 = { a, aa, aaa, aaaa, … } = { a\u207f | n \u2265 1 }<\/span><\/p>\n This language is regular and can be represented by the regular expression a\u207a<\/strong>.<\/span><\/p>\n However, consider a different example:<\/p>\n Let L\u2099 = { a\u207fb\u207f } for each n \u2265 1. Each L\u2099 is finite and thus regular. Now, consider the union:<\/p>\n L = \u22c3\u2099\u208c\u2081^\u221e L\u2099 = { ab, aabb, aaabbb, … } = { a\u207fb\u207f | n \u2265 1 }<\/span><\/p>\n This language is not<\/strong> regular, as it requires matching numbers of a’s and b’s, which cannot be done with a finite automaton.<\/span><\/p>\n Therefore, the infinite union of regular languages is not necessarily<\/strong> regular, indicating that the class of regular languages is not closed<\/strong> under infinite union.<\/span><\/p>\n If you’re interested in exploring more questions from GATE 1989 or other years, or if you need further clarification on topics within the Theory of Computation, feel free to ask!<\/p>\n GATE 1989 Subject – Theory Of Computation Topic -Finite Automata [fvplayer id=”154″] Here’s a focused breakdown of the GATE 1989 paper, particularly for the Theory of Computation subject under the topic Finite Automata: \ud83d\udcdd GATE 1989 \u2013 Theory of Computation \ud83d\udcda Topic: Finite Automata \ud83d\udd39 Key Concepts to Revise Before jumping into specific questions or […]<\/p>\n","protected":false},"author":71,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-2875","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2875","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=2875"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2875\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=2875"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=2875"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=2875"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\ud83d\udcdd GATE 1989 \u2013 Theory of Computation<\/strong><\/h2>\n
\ud83d\udcda Topic: Finite Automata<\/strong><\/h3>\n
\ud83d\udd39 Key Concepts to Revise<\/strong><\/h3>\n
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\n\ud83d\udccc Sample GATE 1989 Style Question (Finite Automata)<\/strong><\/h3>\n
Which of the following statements is true<\/strong>?<\/p>\n
b) Every DFA is also an NFA
c) Every regular language is not accepted by DFA
d) NFA can recognize non-regular languages<\/p>\n\n
Option (a) is false because not all NFAs are DFAs without conversion.
Option (c) is false because every regular language is accepted by a DFA<\/strong>.
Option (d) is false because NFAs cannot recognize non-regular languages<\/strong>.<\/p>\n<\/blockquote>\n
\n\ud83e\udde0 Conceptual Question Example<\/strong><\/h3>\n
Let L be a language accepted by a DFA. Which of the following statements is true?<\/p>\n
b) Complement of L is not regular
c) L is regular
d) L cannot be described by a regular expression<\/p>\n\n
\n\ud83d\udccc Useful Tips for Finite Automata Questions in GATE<\/strong><\/h3>\n
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\n\ud83d\udcd8 Recommended Practice Problems<\/strong><\/h3>\n
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{0,1}<\/code> that end with 01<\/code>.<\/p>\n<\/li>\n
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\n\ud83d\udcd8 GATE 1989 \u2013 Theory of Computation<\/strong><\/h3>\n
\ud83e\udde0 Topic: Finite Automata<\/strong><\/h4>\n
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\nGATE 1989 Subject – Theory Of Computation Topic -Finite Automata<\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"