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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

30 votes
6 answers
6502
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^*$$0(00)^*$(i) and (ii)(ii) a...
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26 votes
5 answers
6504
GATE CSE 1995 | Question: 2.24
Let $\Sigma=\left\{0,1\right\}, L = \Sigma^*$ and $R=\left\{0^n1^n \mid n > 0\right\} $ then the languages $L \cup R$ and $R$ are respectively regular, regular not regular, regular regular, not regular not regular, not regular
Let $\Sigma=\left\{0,1\right\}, L = \Sigma^*$ and $R=\left\{0^n1^n \mid n 0\right\} $ then the languages $L \cup R$ and $R$ are respectivelyregular, regularnot regular, ...
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41 votes
5 answers
6505
GATE CSE 1995 | Question: 2.23
A finite state machine with the following state table has a single input $x$ and a single out $z$ ... $C$ is: $01$ $10$ $101$ $110$
A finite state machine with the following state table has a single input $x$ and a single out $z$.$$\begin{array}{|c|ll|}\hline\textbf{present state} & \qquad \textbf{nex...
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32 votes
8 answers
6506
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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70 votes
3 answers
6509
GATE CSE 1994 | Question: 3.3
State True or False with one line explanation A FSM (Finite State Machine) can be designed to add two integers of any arbitrary length (arbitrary number of digits).
State True or False with one line explanationA FSM (Finite State Machine) can be designed to add two integers of any arbitrary length (arbitrary number of digits).
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33 votes
5 answers
6510
GATE CSE 1994 | Question: 2.10
The regular expression for the language recognized by the finite state automaton of figure is ________
The regular expression for the language recognized by the finite state automaton of figure is ________
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4 votes
1 answer
6512
Toc theorem proof
How $\phi^*=\epsilon$?
How $\phi^*=\epsilon$?
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62 votes
9 answers
6513
GATE CSE 2010 | Question: 41
Let $w$ be any string of length $n$ in $\{0,1\}^*$. Let $L$ be the set of all substrings of $w$. What is the minimum number of states in non-deterministic finite automation that accepts $L$? $n-1$ $n$ $n+1$ $2^{n-1}$
Let $w$ be any string of length $n$ in $\{0,1\}^*$. Let $L$ be the set of all substrings of $w$. What is the minimum number of states in non-deterministic finite automati...
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32 votes
4 answers
6516
GATE CSE 1993 | Question: 27
Draw the state transition of a deterministic finite state automaton which accepts all strings from the alphabet $\{a,b\}$, such that no string has $3$ consecutive occurrences of the letter $b$.
Draw the state transition of a deterministic finite state automaton which accepts all strings from the alphabet $\{a,b\}$, such that no string has $3$ consecutive occurre...
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24 votes
1 answer
6518
GATE CSE 1997 | Question: 20
Construct a finite state machine with minimum number of states, accepting all strings over $(a,b)$ such that the number of $a$'s is divisible by two and the number of $b$'s is divisible by three.
Construct a finite state machine with minimum number of states, accepting all strings over $(a,b)$ such that the number of $a$'s is divisible by two and the number of $b$...
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