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Regular expressions and finite automata, Context-free grammars and push-down automata, Regular and context-free languages, Pumping lemma, Turing machines and undecidability.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}& \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} & 2 &2&3&3&2&2&2&3&3&3&2&2.5&3
\\\hline\textbf{2 Marks Count} & 3 &3&4&3&3&3&5&3&3&3&3&3.3&5
\\\hline\textbf{Total Marks} & 8 &8&11&9&8&8&12&9&9&9&\bf{8}&\bf{9.1}&\bf{12}\\\hline
\end{array}}}$$

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Most answered questions in Theory of Computation

18 votes
8 answers
21
ISRO2016-38
What is the highest type number that can be assigned to the following grammar? $S\to Aa,A\to Ba,B \to abc$ Type 0 Type 1 Type 2 Type 3
What is the highest type number that can be assigned to the following grammar?$$S\to Aa,A\to Ba,B \to abc$$Type 0Type 1Type 2Type 3
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32 votes
8 answers
25
GATE CSE 1995 | Question: 2.20
Which of the following definitions below generate the same language as $L$, where $L=\{x^ny^n \text{ such that } n\geq 1 \}$? $E \rightarrow xEy\mid xy$ $x y \mid (x^+xyy^+$) $x^+y^+$ I only I and II II and III II only
Which of the following definitions below generate the same language as $L$, where $L=\{x^ny^n \text{ such that } n\geq 1 \}$?$E \rightarrow xEy\mid xy$$x y \mid (x^+xyy^+...
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64 votes
8 answers
26
GATE CSE 1997 | Question: 6.4
Which one of the following regular expressions over $\{0,1\}$ denotes the set of all strings not containing $\text{100}$ as substring? $0^*(1+0)^*$ $0^*1010^*$ $0^*1^*01^*$ $0^*(10+1)^*$
Which one of the following regular expressions over $\{0,1\}$ denotes the set of all strings not containing $\text{100}$ as substring?$0^*(1+0)^*$$0^*1010^*$$0^*1^*01^*$$...
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93 votes
8 answers
27
GATE CSE 2006 | Question: 34
Consider the regular language $L=(111+11111)^{*}.$ The minimum number of states in any DFA accepting this languages is: $3$ $5$ $8$ $9$
Consider the regular language $L=(111+11111)^{*}.$ The minimum number of states in any DFA accepting this languages is:$3$$5$$8$$9$
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42 votes
8 answers
29
GATE CSE 1992 | Question: 02,xvii
Which of the following regular expression identities is/are TRUE? $r^{(^\ast)} =r^\ast$ $(r^\ast s^\ast)=(r+s)^\ast$ $(r+s)^\ast = r^\ast + s^\ast$ $r^\ast s^\ast = r^\ast+s^\ast$
Which of the following regular expression identities is/are TRUE?$r^{(^\ast)} =r^\ast$$(r^\ast s^\ast)=(r+s)^\ast$$(r+s)^\ast = r^\ast + s^\ast$$r^\ast s^\ast = r^\ast+s^...
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1 votes
7 answers
30
UGC NET CSE | January 2017 | Part 3 | Question: 20
Consider the languages $L_{1}= \phi$ and $L_{2}=\{1\}$. Which one of the following represents $L_{1}^{\ast}\cup L_{2}^{\ast} L_{1}^{\ast}$? $\{\in \}$ $\{\in,1\}$ $\phi$ $1^{\ast}$
Consider the languages $L_{1}= \phi$ and $L_{2}=\{1\}$. Which one of the following represents $L_{1}^{\ast}\cup L_{2}^{\ast} L_{1}^{\ast}$?$\{\in \}$$\{\in,1\}$$\phi$$1^{...
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18 votes
7 answers
34
GATE CSE 2020 | Question: 51
Consider the following language. $L = \{{ x\in \{a,b\}^*\mid}$number of $a$’s in $x$ divisible by $2$ but not divisible by $3\}$ The minimum number of states in DFA that accepts $L$ is _________
Consider the following language.$L = \{{ x\in \{a,b\}^*\mid}$number of $a$’s in $x$ divisible by $2$ but not divisible by $3\}$The minimum number of states in DFA that ...
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6 votes
7 answers
37
ISRO2008-7
Consider the grammar $S \rightarrow ABCc \mid bc$ $BA \rightarrow AB$ $Bb \rightarrow bb$ $Ab \rightarrow ab$ $Aa \rightarrow aa$ Which of the following sentences can be derived by this grammar? abc aab abcc abbc
Consider the grammar$S \rightarrow ABCc \mid bc$$BA \rightarrow AB$$Bb \rightarrow bb$$Ab \rightarrow ab$$Aa \rightarrow aa$Which of the following sentences can be derive...
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