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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2021-1}&\textbf{2021-2}&\textbf{2020}&\textbf{2019}&\textbf{2018}&\textbf{2017-1}&\textbf{2017-2}&\textbf{2016-1}&\textbf{2016-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count}&2&3&3&2&2&2&3&3&3&2&2.5&3
\\\hline\textbf{2 Marks Count}&3&4&3&3&3&5&3&3&3&3&3.3&5
\\\hline\textbf{Total Marks}&8&11&9&8&8&12&9&9&9&\bf{8}&\bf{9.2}&\bf{12}\\\hline
\end{array}}}$$

Most answered questions in Theory of Computation

43 votes

14 answers

GATE CSE 2017 Set 1 | Question: 22
Consider the language $L$ given by the regular expression $(a+b)^{*} b (a+b)$ over the alphabet $\{a,b\}$. The smallest number of states needed in a deterministic finite-state automaton (DFA) accepting $L$ is ___________ .

Arjun asked in Theory of Computation Feb 14, 2017

by Arjun

24.0k views

62 votes

13 answers

GATE CSE 2012 | Question: 12
What is the complement of the language accepted by the NFA shown below? Assume $\Sigma = \{a\}$ and $\epsilon$ is the empty string. $\phi$ $\{\epsilon\}$ $a^*$ $\{a , \epsilon\}$

gatecse asked in Theory of Computation Aug 5, 2014

by gatecse

14.6k views

59 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_____________.

makhdoom ghaya asked in Theory of Computation Feb 14, 2015

by makhdoom ghaya

12.9k views

28 votes

11 answers

GATE CSE 2017 Set 2 | Question: 16
Identify the language generated by the following grammar, where $S$ is the start variable. $ S \rightarrow XY$ $ X \rightarrow aX \mid a$ $ Y \rightarrow aYb \mid \epsilon$ $\{a^mb^n \mid m \geq n, n > 0 \}$ $ \{ a^mb^n \mid m \geq n, n \geq 0 \}$ $\{a^mb^n \mid m > n, n \geq 0 \}$ $\{a^mb^n \mid m > n, n > 0 \}$

khushtak asked in Theory of Computation Feb 14, 2017

by khushtak

16.1k views

51 votes

11 answers

GATE CSE 2015 Set 2 | Question: 35
Consider the alphabet $\Sigma = \{0, 1\}$, the null/empty string $\lambda$ and the set of strings $X_0, X_1, \text{ and } X_2$ generated by the corresponding non-terminals of a regular grammar. $X_0, X_1, \text{ and } X_2$ are related as follows. $X_0 = 1 X_1$ $X_1 = 0 X_1 + 1 X_2$ ... $10(0^*+(10)^*)1$ $10(0^*+(10)^*)^*1$ $1(0+10)^*1$ $10(0+10)^*1 +110(0+10)^*1$

go_editor asked in Theory of Computation Feb 12, 2015

by go_editor

14.5k views

53 votes

11 answers

GATE CSE 2003 | Question: 14
The regular expression $0^*(10^*)^*$ denotes the same set as $(1^*0)^*1^*$ $0+(0+10)^*$ $(0+1)^*10(0+1)^*$ None of the above

Kathleen asked in Theory of Computation Sep 16, 2014

by Kathleen

14.3k views

45 votes

11 answers

GATE CSE 2008 | Question: 52
Match the following NFAs with the regular expressions they correspond to: P Q R S $\epsilon + 0\left(01^*1+00\right)^*01^*$ $\epsilon + 0\left(10^*1+00\right)^*0$ $\epsilon + 0\left(10^*1+10\right)^*1$ $\epsilon + 0\left(10^*1+10\right)^*10^*$ $P-2, Q-1, R-3, S-4$ $P-1, Q-3, R-2, S-4$ $P-1, Q-2, R-3, S-4$ $P-3, Q-2, R-1, S-4$

Kathleen asked in Theory of Computation Sep 12, 2014

by Kathleen

9.7k views

67 votes

10 answers

GATE CSE 2017 Set 2 | Question: 39
Let $\delta$ denote the transition function and $\widehat{\delta}$ denote the extended transition function of the $\epsilon$ ... $\emptyset$ $\{q_0, q_1, q_3\}$ $\{q_0, q_1, q_2\}$ $\{q_0, q_2, q_3 \}$

Arjun asked in Theory of Computation Feb 14, 2017

by Arjun

21.5k views

63 votes

10 answers

GATE CSE 2010 | Question: 39
Let $L=\{ w \in \:(0+1)^* \mid w\text{ has even number of }1s \}$. i.e., $L$ is the set of all the bit strings with even numbers of $1$s. Which one of the regular expressions below represents $L$? $(0^*10^*1)^*$ $0^*(10^*10^*)^*$ $0^*(10^*1)^*0^*$ $0^*1(10^*1)^*10^*$

go_editor asked in Theory of Computation Sep 30, 2014

by go_editor

17.5k views

46 votes

9 answers

GATE CSE 2018 | Question: 35
Consider the following languages: $\{a^mb^nc^pd^q \mid m+p=n+q, \text{ where } m, n, p, q \geq 0 \}$ $\{a^mb^nc^pd^q \mid m=n \text{ and }p=q, \text{ where } m, n, p, q \geq 0 \}$ ... Which of the above languages are context-free? I and IV only I and II only II and III only II and IV only

gatecse asked in Theory of Computation Feb 14, 2018

by gatecse

16.2k views

42 votes

9 answers

GATE CSE 2017 Set 2 | Question: 25
The minimum possible number of states of a deterministic finite automaton that accepts the regular language $L$ = {$w_{1}aw_{2}$ | $w_{1},w_{2}$ $\in$ $\left \{ a,b \right \}^{*}$ , $\left | w_{1} \right | = 2, \left | w_{2} \right |\geq 3$} is ______________ .

Madhav asked in Theory of Computation Feb 14, 2017

by Madhav

12.2k views

0 votes

9 answers

Let M range over Turing machine descriptions. Consider the set REG and let the complement of REG be Co-REG.

Purple asked in Theory of Computation Feb 2, 2016

by Purple

375 views

57 votes

9 answers

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 $L$? $n-1$ $n$ $n+1$ $2^{n-1}$

go_editor asked in Theory of Computation Sep 30, 2014

by go_editor

19.3k views

37 votes

9 answers

GATE CSE 1991 | Question: 17,b
Let $L$ be the language of all binary strings in which the third symbol from the right is a $1$. Give a non-deterministic finite automaton that recognizes $L$. How many states does the minimized equivalent deterministic finite automaton have? Justify your answer briefly?

Kathleen asked in Theory of Computation Sep 13, 2014

by Kathleen

9.4k views

45 votes

8 answers

GATE CSE 2017 Set 1 | Question: 37
Consider the context-free grammars over the alphabet $\left \{ a, b, c \right \}$ given below. $S$ and $T$ are non-terminals. $G_{1}:S\rightarrow aSb \mid T, T \rightarrow cT \mid \epsilon$ ... is Finite Not finite but regular Context-Free but not regular Recursive but not context-free

Arjun asked in Theory of Computation Feb 14, 2017

by Arjun

9.6k views

67 votes

8 answers

GATE CSE 2017 Set 1 | Question: 10
Consider the following context-free grammar over the alphabet $\Sigma = \{a,b,c\}$ with $S$ as the start symbol:$S \rightarrow abScT \mid abcT$$T \rightarrow bT \mid b$ ... $\{\left ( ab \right )^{n}\left ( cb^{n} \right )^{m} \mid m,n \geq 1 \}$

Arjun asked in Theory of Computation Feb 14, 2017

by Arjun

17.0k views

3 votes

8 answers

UGC NET CSE | June 2016 | Part 3 | Question: 55
Let L be the language generated by regular expression 0*10* and accepted by the deterministic finite automata M. Consider the relation $R_M$ defined by M as all states that are reachable from the start state. $R_M$ has ___ equivalence classes. 2 4 5 6

go_editor asked in Theory of Computation Aug 20, 2016

by go_editor

5.9k views

18 votes

8 answers

ISRO2016-38
What is the highest type number that can be assigned to the following grammar? $S\to Aa,A\to Ba,B \to abc$ Type 0 Type 1 Type 2 Type 3

Anu asked in Theory of Computation Jul 4, 2016

by Anu

15.5k views

47 votes

8 answers

GATE IT 2004 | Question: 40
Let $M = (K, Σ, Г, Δ, s, F)$ be a pushdown automaton, where $K = (s, f), F = \{f\}, \Sigma = \{a, b\}, Г = \{a\}$ and $Δ = \{((s, a, \epsilon), (s, a)), ((s, b, \epsilon), (s, a)), (( s, a, a), (f, \epsilon)), ((f, a, a), (f, \epsilon)), ((f, b, a), (f, \epsilon))\}$. Which one of the following strings is not a member of $L(M)$? $aaa$ $aabab$ $baaba$ $bab$

Ishrat Jahan asked in Theory of Computation Nov 2, 2014

by Ishrat Jahan

15.7k views

36 votes

8 answers

GATE IT 2007 | Question: 73
Consider the regular expression $R = (a + b)^* \ (aa + bb) \ (a + b)^*$ Which one of the regular expressions given below defines the same language as defined by the regular expression $R$ ? $(a(ba)^* + b(ab)^*)(a + b)^+$ $(a(ba)^* + b(ab)^*)^*(a + b)^*$ $(a(ba)^* (a + bb) + b(ab)^*(b + aa))(a + b)^*$ $(a(ba)^* (a + bb) + b(ab)^*(b + aa))(a + b)^+$

Ishrat Jahan asked in Theory of Computation Oct 31, 2014

by Ishrat Jahan

11.5k views

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