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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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Previous GATE Questions in Theory of Computation

36 votes
6 answers
101
GATE CSE 2015 Set 2 | Question: 53
The number of states in the minimal deterministic finite automaton corresponding to the regular expression $(0+1)^* (10)$ is _____.
The number of states in the minimal deterministic finite automaton corresponding to the regular expression $(0+1)^* (10)$ is _____.
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29 votes
5 answers
108
GATE CSE 1998 | Question: 3b
Give a regular expression for the set of binary strings where every $0$ is immediately followed by exactly $k$ $1$'s and preceded by at least $k$ $1$’s ($k$ is a fixed integer)
Give a regular expression for the set of binary strings where every $0$ is immediately followed by exactly $k$ $1$'s and preceded by at least $k$ $1$’s ($k$ is a fixed...
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17 votes
2 answers
109
GATE CSE 1996 | Question: 13
Let $Q=\left( \left\{q_1,q_2 \right\}, \left\{a,b\right \}, \left\{a,b,\bot \right\}, \delta, \bot, \phi \right)$ ... $\delta(q_2,b,b) = \left\{(q_2, \epsilon)\right\}$ $\delta(q_2,\epsilon,\bot) = \left\{(q_2, \epsilon)\right\}$
Let $Q=\left( \left\{q_1,q_2 \right\}, \left\{a,b\right \}, \left\{a,b,\bot \right\}, \delta, \bot, \phi \right)$ be a pushdown automaton accepting by empty stack for the...
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23 votes
6 answers
112
GATE CSE 1996 | Question: 2.8
If $L_1$ and $L_2$ are context free languages and $R$ a regular set, one of the languages below is not necessarily a context free language. Which one? $L_1.L_2$ $L_1 \cap L_2$ $L_1 \cap R$ $L_1 \cup L_2$
If $L_1$ and $L_2$ are context free languages and $R$ a regular set, one of the languages below is not necessarily a context free language. Which one?$L_1.L_2$$L_1 \cap L...
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30 votes
6 answers
115
GATE CSE 1996 | Question: 1.8
Which two of the following four regular expressions are equivalent? ($\varepsilon$ is the empty string). $(00)^ * (\varepsilon +0)$ $(00)^*$ $0^*$ $0(00)^*$ (i) and (ii) (ii) and (iii) (i) and (iii) (iii) and (iv)
Which two of the following four regular expressions are equivalent? ($\varepsilon$ is the empty string).$(00)^ * (\varepsilon +0)$$(00)^*$$0^*$$0(00)^*$(i) and (ii)(ii) a...
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26 votes
5 answers
117
GATE CSE 1995 | Question: 2.24
Let $\Sigma=\left\{0,1\right\}, L = \Sigma^*$ and $R=\left\{0^n1^n \mid n > 0\right\} $ then the languages $L \cup R$ and $R$ are respectively regular, regular not regular, regular regular, not regular not regular, not regular
Let $\Sigma=\left\{0,1\right\}, L = \Sigma^*$ and $R=\left\{0^n1^n \mid n 0\right\} $ then the languages $L \cup R$ and $R$ are respectivelyregular, regularnot regular, ...
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41 votes
5 answers
118
GATE CSE 1995 | Question: 2.23
A finite state machine with the following state table has a single input $x$ and a single out $z$ ... $C$ is: $01$ $10$ $101$ $110$
A finite state machine with the following state table has a single input $x$ and a single out $z$.$$\begin{array}{|c|ll|}\hline\textbf{present state} & \qquad \textbf{nex...
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32 votes
8 answers
119
GATE CSE 1995 | Question: 2.20
Which of the following definitions below generate the same language as $L$, where $L=\{x^ny^n \text{ such that } n\geq 1 \}$? $E \rightarrow xEy\mid xy$ $x y \mid (x^+xyy^+$) $x^+y^+$ I only I and II II and III II only
Which of the following definitions below generate the same language as $L$, where $L=\{x^ny^n \text{ such that } n\geq 1 \}$?$E \rightarrow xEy\mid xy$$x y \mid (x^+xyy^+...
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