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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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Recent questions in Theory of Computation

19 votes
5 answers
6485
ISRO2014-2
The number of states required by a Finite State Machine,to simulate the behavior of a computer with a memory capable of storing 'm' words, each of length 'n' bits is? $m \times 2^n$ $2^{m+n}$ $2^{mn}$ $m+n$
The number of states required by a Finite State Machine,to simulate the behavior of a computer with a memory capable of storing 'm' words, each of length 'n' bits is?$m \...
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56 votes
6 answers
6486
GATE IT 2008 | Question: 36
Consider the following two finite automata. $M_1$ accepts $L_1$ and $M_2$ accepts $L_2$. $M_1$ $M_2$ Which one of the following is TRUE? $L_1 = L_2$ $L_1 \subset L_2$ $L_1 \cap L_{2}^{C} = \varnothing $ $L_1 \cup L_2 \neq L_1$
Consider the following two finite automata. $M_1$ accepts $L_1$ and $M_2$ accepts $L_2$.$M_1$$M_2$ Which one of the following is TRUE?$L_1 = L_2$$L_1 \subset L_2$$L_1 \ca...
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44 votes
7 answers
6488
GATE IT 2008 | Question: 34
Consider a CFG with the following productions. $S \to AA \mid B$ $A \to 0A \mid A0 \mid 1$ $B \to 0B00 \mid 1$ $S$ is the start symbol, $A$ and $B$ ... $\{0, 1\}$ containing at least two $0$'s
Consider a CFG with the following productions.$S \to AA \mid B$$A \to 0A \mid A0 \mid 1$$B \to 0B00 \mid 1$$S$ is the start symbol, $A$ and $B$ are non-terminals and 0 an...
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30 votes
5 answers
6491
GATE IT 2008 | Question: 6
Let $N$ be an NFA with $n$ states and let $M$ be the minimized DFA with m states recogniz­ing the same language. Which of the following in NECESSARILY true? $m \leq 2^n$ $n \leq m$ $M$ has one accept state $m = 2^n$
Let $N$ be an NFA with $n$ states and let $M$ be the minimized DFA with m states recogniz­ing the same language. Which of the following in NECESSARILY true?$m \leq 2^n$$...
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23 votes
3 answers
6492
GATE IT 2008 | Question: 5
Which of the following regular expressions describes the language over$\{0, 1\}$ consisting of strings that contain exactly two $1$'s? $(0 + 1)^ * \ 11(0 + 1) ^*$ $0 ^* \ 110 ^*$ $0 ^* 10 ^* 10 ^*$ $(0 + 1) ^* 1(0 + 1) ^* 1 (0 + 1) ^*$
Which of the following regular expressions describes the language over$\{0, 1\}$ consisting of strings that contain exactly two $1$'s?$(0 + 1)^ * \ 11(0 + 1) ^*$$0 ^* \ 1...
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1 votes
1 answer
6493
Regular or not ?
{ wxw | w belongs to {0,1}* , x belongs to {0,1}+ }
{ wxw | w belongs to {0,1}* , x belongs to {0,1}+ }
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29 votes
5 answers
6495
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
6496
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
6499
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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