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

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

Previous GATE Questions in Theory of Computation

27 votes

3 answers

GATE CSE 2007 | Question: 75
Consider the following Finite State Automaton: The minimum state automaton equivalent to the above FSA has the following number of states: $1$ $2$ $3$ $4$

Consider the following Finite State Automaton:The minimum state automaton equivalent to the above FSA has the following number of states:$1$$2$$3$$4$

go_editor

8.5k views

go_editor asked Apr 23, 2016

48 votes

6 answers

GATE CSE 2016 Set 1 | Question: 43
Consider the transition diagram of a PDA given below with input alphabet $\Sigma=\{a,b\}$ and stack alphabet $\Gamma = \{X,Z\}$. $Z$ is the initial stack symbol. Let $L$ ... on every input $L =\{a^n\mid n \geq0 \} \cup \{a^nb^n \mid n \geq 0\}$ and is deterministic context-free

Consider the transition diagram of a PDA given below with input alphabet $\Sigma=\{a,b\}$ and stack alphabet $\Gamma = \{X,Z\}$. $Z$ is the initial stack symbol. Let $L$ ...

Sandeep Singh

16.9k views

Sandeep Singh asked Feb 12, 2016

47 votes

5 answers

GATE CSE 2016 Set 1 | Question: 44
Let $X$ be a recursive language and $Y$ be a recursively enumerable but not recursive language. Let $W$ and $Z$ be two languages such that $\overline{Y}$ reduces to $W$, and $Z$ reduces to $\overline{X}$ (reduction means the standard ... enumerable. $W$ is not recursively enumerable and $Z$ is recursive. $W$ is not recursively enumerable and $Z$ is not recursive.

Let $X$ be a recursive language and $Y$ be a recursively enumerable but not recursive language. Let $W$ and $Z$ be two languages such that $\overline{Y}$ reduces to $W$,...

Sandeep Singh

12.4k views

Sandeep Singh asked Feb 12, 2016

59 votes

8 answers

GATE CSE 2016 Set 1 | Question: 42
Consider the following context-free grammars; $G_1 : S \to aS \mid B, B \to b \mid bB$ $G_2 : S \to aA \mid bB, A \to aA \mid B \mid \varepsilon,B \to bB \mid \varepsilon$ Which one of the following pairs of languages is generated by $G_1$ and $G_2$ ... $\{ a^mb^n \mid m > 0 \text{ or } n>0\}$

Consider the following context-free grammars;$G_1 : S \to aS \mid B, B \to b \mid bB$$G_2 : S \to aA \mid bB, A \to aA \mid B \mid \varepsilon,B \to bB \mid \varepsilon$W...

Sandeep Singh

26.8k views

Sandeep Singh asked Feb 12, 2016

32 votes

4 answers

GATE CSE 2016 Set 1 | Question: 17
Which of the following decision problems are undecidable? Given NFAs $N_1$ and $N_2$ , is $L(N_1) \cap L(N_2) = \Phi$ Given a CFG $G = (N,\Sigma,P,S)$ and a string $x \in \Sigma^{*}$, does $x \in L(G)$} ? Given CFGs $G_1$ and $G_2$, is $L (G_1) = L(G_2)$? Given a TM $M$, is $L(M)=\Phi$ ? I and IV only II and III only III and IV only II and IV only

Which of the following decision problems are undecidable?Given NFAs $N_1$ and $N_2$ , is $L(N_1) \cap L(N_2) = \Phi$Given a CFG $G = (N,\Sigma,P,S)$ and a string $x \in ...

Sandeep Singh

8.6k views

Sandeep Singh asked Feb 12, 2016

57 votes

4 answers

GATE CSE 2016 Set 1 | Question: 18
Which one of the following regular expressions represents the language: the set of all binary strings having two consecutive $0$'s and two consecutive $1$'s? $(0+1 )^ *0011 (0+1)^* +(0+1)^*1100(0+1)^*$ $(0+1)^* (00(0+1)^*11+11(0+1)^*00)(0+1)^*$ $(0+1)^*00(0+1)^* + (0+1)^*11 (0+1)^*$ $00(0+1)^*11 +11(0+1)^*00$

Which one of the following regular expressions represents the language: the set of all binary strings having two consecutive $0$'s and two consecutive $1$'s?$(0+1 )^ *001...

Sandeep Singh

20.8k views

Sandeep Singh asked Feb 12, 2016

51 votes

5 answers

GATE CSE 2016 Set 1 | Question: 16
Which of the following languages is generated by the given grammar? $S \rightarrow aS \mid bS \mid \varepsilon$ $\{ a^nb^m \mid n,m \geq 0\}$ $\{ w \in \{ a,b\}^* \mid w\text{ has equal number of a's and b's}\}$ $\{a^n \mid n \geq 0 \} \cup \{b^n \mid n \geq 0\} \cup \{a^n b^n \mid n \geq 0\}$ $\{ a,b\}^*$

Which of the following languages is generated by the given grammar?$$S \rightarrow aS \mid bS \mid \varepsilon$$$\{ a^nb^m \mid n,m \geq 0\}$$\{ w \in \{ a,b\}^* \mid w\t...

Sandeep Singh

12.1k views

Sandeep Singh asked Feb 12, 2016

50 votes

5 answers

GATE CSE 2016 Set 2 | Question: 43
Consider the following languages: $L_{1}=\left\{a^{n}b^{m}c^{n+m}:m, n\geq 1\right\}$ $L_{2}=\left\{a^{n}b^{n}c^{2n} :n\geq 1\right\}$ Which one of the following is TRUE? Both $L_{1}$ and $L_{2}$ are context-free. $L_{1}$ is context ... $L_{2}$ is context-free while $L_{1}$ is not context-free. Neither $L_{1}$ nor $L_{2}$ is context-free.

Consider the following languages:$L_{1}=\left\{a^{n}b^{m}c^{n+m}:m, n\geq 1\right\}$$L_{2}=\left\{a^{n}b^{n}c^{2n} :n\geq 1\right\}$Which one of the following is TRUE?Bot...

Akash Kanase

21.5k views

Akash Kanase asked Feb 12, 2016

108 votes

7 answers

GATE CSE 2016 Set 2 | Question: 44
Consider the following languages. $L_{1} = \left\{\left\langle M \right\rangle \mid M \text{ takes at least 2016 steps on some input} \right\}$ ... not recursive $L_{1}, L_{2}$ are recursive and $L_{3}$ is not recursive $L_{1}, L_{2}, L_{3}$ are recursive

Consider the following languages.$L_{1} = \left\{\left\langle M \right\rangle \mid M \text{ takes at least 2016 steps on some input} \right\}$,$L_{2} = \left\{\left\langl...

Akash Kanase

33.5k views

Akash Kanase asked Feb 12, 2016

79 votes

3 answers

GATE CSE 2016 Set 2 | Question: 42
Consider the following two statements: If all states of an NFA are accepting states then the language accepted by the NFA is $\Sigma_{}^{*}$. There exists a regular language $A$ such that for all languages $B$, $A \cap B$ is regular. Which one of the following is CORRECT? Only I is true Only II is true Both I and II are true Both I and II are false

Consider the following two statements:If all states of an NFA are accepting states then the language accepted by the NFA is $\Sigma_{}^{*}$.There exists a regular languag...

Akash Kanase

25.6k views

Akash Kanase asked Feb 12, 2016

48 votes

2 answers

GATE CSE 2016 Set 2 | Question: 18
Consider the following types of languages: $L_{1}$: Regular, $L_{2}$: Context-free, $L_{3}$: Recursive, $L_{4}$: Recursively enumerable. Which of the following is/are TRUE ? $\overline{L_{3}} \cup L_{4}$ ... is context-free. I only. I and III only. I and IV only. I, II and III only.

Consider the following types of languages: $L_{1}$: Regular, $L_{2}$: Context-free, $L_{3}$: Recursive, $L_{4}$: Recursively enumerable. Which of the following is/are TRU...

Akash Kanase

12.1k views

Akash Kanase asked Feb 12, 2016

38 votes

5 answers

GATE CSE 2016 Set 2 | Question: 16
The number of states in the minimum sized DFA that accepts the language defined by the regular expression. $(0+1)^{*} (0+1) (0+1)^{*}$ is ________.

The number of states in the minimum sized DFA that accepts the language defined by the regular expression.$(0+1)^{*} (0+1) (0+1)^{*}$is ________.

Akash Kanase

15.8k views

Akash Kanase asked Feb 12, 2016

22 votes

2 answers

GATE CSE 2016 Set 2 | Question: 17
Language $L_{1}$ is defined by the grammar: $S_{1} \rightarrow a S_{1} b \mid \varepsilon$ Language $L_{2}$ is defined by the grammar: $S_{2} \rightarrow a b S_{2} \mid \varepsilon$ Consider the following statements: P: $L_{1}$ is regular Q: $L_{2}$ is regular ... $Q$ are true. $P$ is true and $Q$ is false. $P$ is false and $Q$ is true. Both $P$ and $Q$ are false.

Language $L_{1}$ is defined by the grammar: $S_{1} \rightarrow a S_{1} b \mid \varepsilon$Language $L_{2}$ is defined by the grammar: $S_{2} \rightarrow a b S_{2} \mid \v...

Akash Kanase

7.8k views

Akash Kanase asked Feb 12, 2016

21 votes

5 answers

GATE CSE 1991 | Question: 17,a
Show that the Turing machines, which have a read only input tape and constant size work tape, recognize precisely the class of regular languages.

Show that the Turing machines, which have a read only input tape and constant size work tape, recognize precisely the class of regular languages.

Arjun

5.8k views

Arjun asked Nov 15, 2015

21 votes

2 answers

GATE CSE 1997 | Question: 70
Following is a state table for time finite state machine. ... . For example if states $X$ and $Y$ are equivalent then use $XY$ as the name for the equivalent state in the minimal machine).

Following is a state table for time finite state machine.$$\begin{array}{|l|ll|}\hline \textbf{Present State} & \textbf{Next State Output} \\ & \textbf{Input- 0} & \t...

go_editor

7.8k views

go_editor asked Oct 14, 2015

38 votes

4 answers

GATE CSE 2015 Set 3 | Question: 53
Language $L_1$ is polynomial time reducible to language $L_2$. Language $L_3$ is polynomial time reducible to language $L_2$, which in turn polynomial time reducible to language $L_4$. Which of the following is/are true? $\text{ if } L_4 \in P, \text{ then } L_2 \in P$ ... $\text{ if } L_4 \in P, \text{ then } L_3 \in P$ II only III only I and IV only I only

Language $L_1$ is polynomial time reducible to language $L_2$. Language $L_3$ is polynomial time reducible to language $L_2$, which in turn polynomial time reducible to l...

go_editor

9.1k views

go_editor asked Feb 16, 2015

44 votes

2 answers

GATE CSE 2015 Set 3 | Question: 32
Which of the following languages are context-free? $L_1: \left\{a^mb^na^nb^m \mid m, n \geq 1\right\}$ $L_2: \left\{a^mb^na^mb^n \mid m, n \geq 1\right\}$ $L_3: \left\{a^mb^n \mid m = 2n +1 \right\}$ $L_1$ and $L_2$ only $L_1$ and $L_3$ only $L_2$ and $L_3$ only $L_3$ only

Which of the following languages are context-free?$L_1: \left\{a^mb^na^nb^m \mid m, n \geq 1\right\}$$L_2: \left\{a^mb^na^mb^n \mid m, n \geq 1\right\}$$L_3: \left\{a^mb^...

go_editor

15.0k views

go_editor asked Feb 15, 2015

55 votes

5 answers

GATE CSE 2015 Set 3 | Question: 18
Let $L$ be the language represented by the regular expression $\Sigma^*0011\Sigma^*$ where $\Sigma = \{0, 1\}$. What is the minimum number of states in a DFA that recognizes $\bar{L}$ (complement of $L$)? $4$ $5$ $6$ $8$

Let $L$ be the language represented by the regular expression $\Sigma^*0011\Sigma^*$ where $\Sigma = \{0, 1\}$. What is the minimum number of states in a DFA that recogni...

go_editor

17.1k views

go_editor asked Feb 14, 2015

65 votes

12 answers

GATE CSE 2015 Set 1 | Question: 52
Consider the DFAs $M$ and $N$ given above. The number of states in a minimal DFA that accept the language $L(M) \cap L(N)$ is_____________.

Consider the DFAs $M$ and $N$ given above. The number of states in a minimal DFA that accept the language $L(M) \cap L(N)$ is_____________.

makhdoom ghaya

17.2k views

makhdoom ghaya asked Feb 13, 2015

83 votes

4 answers

100

GATE CSE 2015 Set 1 | Question: 51
Consider the NPDA ... follows: Which one of the following sequences must follow the string $101100$ so that the overall string is accepted by the automaton? $10110$ $10010$ $01010$ $01001$

Consider the NPDA $$ \left \langle Q= \left \{ q_{0}, q_{1}, q_{2} \right \},\Sigma = \left \{ 0, 1 \right \}, \Gamma = \left \{ 0, 1, \perp \right \}, \delta, q_{0}, \p...

makhdoom ghaya

23.8k views

makhdoom ghaya asked Feb 13, 2015

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