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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
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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42 votes
7 answers
41
GATE IT 2007 | Question: 72
Consider the regular expression $R = (a + b)^* (aa + bb) (a + b)^*$ Which deterministic finite automaton accepts the language represented by the regular expression $R$?
Consider the regular expression $R = (a + b)^* (aa + bb) (a + b)^*$Which deterministic finite automaton accepts the language represented by the regular expression $R$?
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44 votes
7 answers
42
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$$S$ is the start symbol, $A$ and $B$ are non-terminals and 0 an...
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41 votes
7 answers
44
GATE CSE 1998 | Question: 1.12
The string $1101$ does not belong to the set represented by $110^*(0 + 1)$ $1(0 + 1)^*101$ $(10)^*(01)^*(00 + 11)^*$ $(00 + (11)^*0)^*$
The string $1101$ does not belong to the set represented by$110^*(0 + 1)$$1(0 + 1)^*101$$(10)^*(01)^*(00 + 11)^*$$(00 + (11)^*0)^*$
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46 votes
7 answers
46
GATE CSE 2009 | Question: 41
The above DFA accepts the set of all strings over $\{0,1\}$ that begin either with $0$ or $1$. end with $0$. end with $00$. contain the substring $00$.
The above DFA accepts the set of all strings over $\{0,1\}$ that begin either with $0$ or $1$.end with $0$.end with $00$.contain the substring $00$.
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20 votes
6 answers
50
GATE CSE 2021 Set 2 | Question: 17
Consider the following deterministic finite automaton $\text{(DFA)}$ The number of strings of length $8$ accepted by the above automaton is ___________
Consider the following deterministic finite automaton $\text{(DFA)}$The number of strings of length $8$ accepted by the above automaton is ___________
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