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

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1} & \textbf{2024-2} & \textbf{2023} & \textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &1&1&3& 2 &2&3& 1&2&3
\\\hline\textbf{2 Marks Count} &2&3&3& 3 &3&4& 2&3&4
\\\hline\textbf{Total Marks} &5&7&9& 8 &8&11&\bf{5}&\bf{8}&\bf{11}\\\hline
\end{array}}}$$

Highest voted questions in Theory of Computation

36 votes

4 answers

121

GATE CSE 2017 Set 2 | Question: 40
Consider the following languages. $L_1 = \{a^p \mid p \text{ is a prime number} \}$ $L_2 = \{ a^nb^mc^{2m} \mid n \geq 0, m \geq 0 \}$ $L_3 = \{a^n b^n c^{2n} \mid n \geq 0 \}$ ... not context free $L_3$ is not context free but recursive $L_4$ is deterministic context free I, II and IV only II and III only I and IV only III and IV only

Consider the following languages.$L_1 = \{a^p \mid p \text{ is a prime number} \}$$L_2 = \{ a^nb^mc^{2m} \mid n \geq 0, m \geq 0 \}$$L_3 = \{a^n b^n c^{2n} \mid n \geq 0 ...

Madhav

9.0k views

Madhav asked Feb 14, 2017

36 votes

6 answers

122

GATE CSE 2015 Set 2 | Question: 53
The number of states in the minimal deterministic finite automaton corresponding to the regular expression $(0+1)^* (10)$ is _____.

The number of states in the minimal deterministic finite automaton corresponding to the regular expression $(0+1)^* (10)$ is _____.

go_editor

15.8k views

go_editor asked Feb 13, 2015

36 votes

6 answers

123

GATE CSE 2011 | Question: 45
A deterministic finite automaton ($\text{DFA}$) $D$ with alphabet $\Sigma = \{a, b\}$ is given below. Which of the following finite state machines is a valid minimal $\text{DFA}$ which accepts the same languages as $D$?

A deterministic finite automaton ($\text{DFA}$) $D$ with alphabet $\Sigma = \{a, b\}$ is given below.Which of the following finite state machines is a valid minimal $\tex...

go_editor

10.9k views

go_editor asked Sep 29, 2014

36 votes

4 answers

124

GATE CSE 2011 | Question: 26
Consider the languages $L1, \:L2 \:and \: L3$ ... Automata (PDA) can be used to recognize $L1$ and $L2$ $L1$ is a regular language All the three languages are context free Turing machines can be used to recognize all the languages

Consider the languages $L1, \:L2 \:and \: L3$ as given below.$L1=\{0^p 1^q \mid p, q \in N\}, \\ L2 = \{0^p 1^q \mid p, q \in N \:and \:p=q\} \: and, \\ L3 = \{0^p 1^q 0^...

go_editor

9.5k views

go_editor asked Sep 29, 2014

36 votes

2 answers

125

GATE CSE 1998 | Question: 4
Design a deterministic finite state automaton (using minimum number of states) that recognizes the following language: $L=\{w \in \{0, 1\}^* \mid w$ interpreted as binary number (ignoring the leading zeros) is divisible by five $\}.$

Design a deterministic finite state automaton (using minimum number of states) that recognizes the following language:$L=\{w \in \{0, 1\}^* \mid w$ interpreted as binar...

Kathleen

11.9k views

Kathleen asked Sep 25, 2014

36 votes

5 answers

126

GATE CSE 2005 | Question: 57
Consider the languages: $L_1 = \left\{ww^R \mid w \in \{0, 1\}^* \right\}$ $L_2 = \left\{w\text{#}w^R \mid w \in \{0, 1\}^* \right\}$, where $\text{#}$ ... of the following is TRUE? $L_1$ is a deterministic CFL $L_2$ is a deterministic CFL $L_3$ is a CFL, but not a deterministic CFL $L_3$ is a deterministic CFL

Consider the languages:$L_1 = \left\{ww^R \mid w \in \{0, 1\}^* \right\}$$L_2 = \left\{w\text{#}w^R \mid w \in \{0, 1\}^* \right\}$, where $\text{#}$ is a special symbol$...

Kathleen

8.6k views

Kathleen asked Sep 22, 2014

36 votes

2 answers

127

GATE CSE 2001 | Question: 5
Construct DFA's for the following languages: $L=\left\{w \mid w \in \{a,b\}^*, \text{ w has baab as a substring } \right\}$ $L=\left\{w \mid w \in \{a,b\}^*, \text{ w has an odd number of a's and an odd number of b's } \right\} $

Construct DFA's for the following languages:$L=\left\{w \mid w \in \{a,b\}^*, \text{ w has baab as a substring } \right\}$$L=\left\{w \mid w \in \{a,b\}^*, \text{ w has ...

Kathleen

5.4k views

Kathleen asked Sep 14, 2014

35 votes

4 answers

128

GATE CSE 2019 | Question: 34
Consider the following sets: S1: Set of all recursively enumerable languages over the alphabet $\{0, 1\}$ S2: Set of all syntactically valid C programs S3: Set of all languages over the alphabet $\{0,1\}$ S4: Set of all non-regular languages over the alphabet $\{ 0,1 \}$ Which of the above sets are uncountable? S1 and S2 S3 and S4 S2 and S3 S1 and S4

Consider the following sets:S1: Set of all recursively enumerable languages over the alphabet $\{0, 1\}$S2: Set of all syntactically valid C programsS3: Set of all langua...

Arjun

13.2k views

Arjun asked Feb 7, 2019

35 votes

2 answers

129

GATE IT 2008 | Question: 33
Consider the following languages. $L_1 = \{a^i b^j c^k \mid i = j, k \geq 1\}$ $L_2 = \{a^i b^j \mid j = 2i, i \geq 0\}$ Which of the following is true? $L_1$ is not a CFL but $L_2$ is $L_1 \cap L_2 = \varnothing $ and $L_1$ is non-regular $L_1 \cup L_2$ is not a CFL but $L_2$ is There is a $4$-state PDA that accepts $L_1$, but there is no DPDA that accepts $L_2$.

Consider the following languages.$L_1 = \{a^i b^j c^k \mid i = j, k \geq 1\}$$L_2 = \{a^i b^j \mid j = 2i, i \geq 0\}$Which of the following is true?$L_1$ is not a CFL bu...

Ishrat Jahan

6.1k views

Ishrat Jahan asked Oct 28, 2014

35 votes

4 answers

130

GATE IT 2008 | Question: 32
If the final states and non-final states in the DFA below are interchanged, then which of the following languages over the alphabet $\{a, b\}$ will be accepted by the new DFA? Set of all strings that do not end with $ab$ Set of all strings that begin ... of all strings that do not contain the substring $ab$, The set described by the regular expression $b^*aa^*(ba)^*b^*$

If the final states and non-final states in the DFA below are interchanged, then which of the following languages over the alphabet $\{a, b\}$ will be accepted by the new...

Ishrat Jahan

9.0k views

Ishrat Jahan asked Oct 28, 2014

35 votes

3 answers

131

GATE CSE 2014 Set 1 | Question: 35
Let $L$ be a language and $\bar{L}$ be its complement. Which one of the following is NOT a viable possibility? Neither $L$ nor $\bar{L}$ is recursively enumerable $(r.e.)$. One of $L$ and $\bar{L}$ is r.e. but not recursive; the other is not r.e. Both $L$ and $\bar{L}$ are r.e. but not recursive. Both $L$ and $\bar{L}$ are recursive.

Let $L$ be a language and $\bar{L}$ be its complement. Which one of the following is NOT a viable possibility?Neither $L$ nor $\bar{L}$ is recursively enumerable $(r.e.)...

go_editor

8.5k views

go_editor asked Sep 26, 2014

34 votes

5 answers

132

GATE CSE 2019 | Question: 7
If $L$ is a regular language over $\Sigma = \{a,b\} $, which one of the following languages is NOT regular? $L.L^R = \{xy \mid x \in L , y^R \in L\}$ $\{ww^R \mid w \in L \}$ $\text{Prefix } (L) = \{x \in \Sigma^* \mid \exists y \in \Sigma^* $such that$ \ xy \in L\}$ $\text{Suffix }(L) = \{y \in \Sigma^* \mid \exists x \in \Sigma^* $such that$ \ xy \in L\}$

If $L$ is a regular language over $\Sigma = \{a,b\} $, which one of the following languages is NOT regular?$L.L^R = \{xy \mid x \in L , y^R \in L\}$$\{ww^R \mid w \in L \...

Arjun

15.0k views

Arjun asked Feb 7, 2019

34 votes

5 answers

133

GATE IT 2006 | Question: 34
In the context-free grammar below, $S$ is the start symbol, $a$ and $b$ are terminals, and $\epsilon$ denotes the empty string. $S \to aSAb \mid \epsilon$ $A \to bA \mid \epsilon$ The grammar generates the language $((a + b)^* b)$ $\{a^mb^n \mid m \leq n\}$ $\{a^mb^n \mid m = n)$ $a^* b^*$

In the context-free grammar below, $S$ is the start symbol, $a$ and $b$ are terminals, and $\epsilon$ denotes the empty string.$S \to aSAb \mid \epsilon$$A \to bA \mid \e...

Ishrat Jahan

8.1k views

Ishrat Jahan asked Oct 31, 2014

34 votes

2 answers

134

GATE CSE 2011 | Question: 24
Let $P$ be a regular language and $Q$ be a context-free language such that $Q \subseteq P$. (For example, let $P$ be the language represented by the regular expression $p^*q^*$ and $Q$ be $\{p^nq^n \mid n \in N\})$. Then which of the following is ALWAYS regular? $P \cap Q$ $P-Q$ $\Sigma^*-P$ $\Sigma^*-Q$

Let $P$ be a regular language and $Q$ be a context-free language such that $Q \subseteq P$. (For example, let $P$ be the language represented by the regular expression $p...

akash

10.0k views

akash asked Oct 29, 2014

34 votes

5 answers

135

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 ________

Kathleen

8.9k views

Kathleen asked Oct 4, 2014

34 votes

4 answers

136

GATE CSE 1997 | Question: 6.5
Which one of the following is not decidable? Given a Turing machine $M$, a string $s$ and an integer $k$, $M$ accepts $s$ within $k$ steps Equivalence of two given Turing machines Language accepted by a given finite state machine is not empty Language generated by a context free grammar is non-empty

Which one of the following is not decidable?Given a Turing machine $M$, a string $s$ and an integer $k$, $M$ accepts $s$ within $k$ stepsEquivalence of two given Turing m...

Kathleen

10.1k views

Kathleen asked Sep 29, 2014

34 votes

2 answers

137

GATE CSE 1999 | Question: 7
Show that the language $L = \left\{ xcx \mid x \in \left\{0,1\right\}^* \text{ and }c\text{ is a terminal symbol}\right\}$ is not context free. $c$ is not $0$ or $1$.

Show that the language $$L = \left\{ xcx \mid x \in \left\{0,1\right\}^* \text{ and }c\text{ is a terminal symbol}\right\}$$ is not context free. $c$ is not $0$ or $1$.

Kathleen

5.2k views

Kathleen asked Sep 23, 2014

34 votes

7 answers

138

GATE CSE 2009 | Question: 12, ISRO2016-37
$S \to aSa \mid bSb\mid a\mid b$ The language generated by the above grammar over the alphabet $\{a,b\}$ is the set of: all palindromes all odd length palindromes strings that begin and end with the same symbol all even length palindromes

$$S \to aSa \mid bSb\mid a\mid b$$The language generated by the above grammar over the alphabet $\{a,b\}$ is the set of:all palindromesall odd length palindromesstrings t...

Kathleen

20.7k views

Kathleen asked Sep 22, 2014

34 votes

2 answers

139

GATE CSE 2008 | Question: 53
Which of the following are regular sets? $\left\{a^nb^{2m} \mid n \geq 0, m \geq 0 \right\}$ $\left\{a^nb^m \mid n =2m \right\}$ $\left\{a^nb^m \mid n \neq m \right\}$ $\left\{xcy \mid x, y, \in \left\{a, b\right\} ^* \right\}$ I and IV only I and III only I only IV only

Which of the following are regular sets?$\left\{a^nb^{2m} \mid n \geq 0, m \geq 0 \right\}$$\left\{a^nb^m \mid n =2m \right\}$$\left\{a^nb^m \mid n \neq m \right\}$$\lef...

Kathleen

9.7k views

Kathleen asked Sep 12, 2014

33 votes

4 answers

140

GATE CSE 2020 | Question: 32
Consider the following languages. $\begin{array}{ll} L_1= \{ wxyx \mid w,x,y \in (0+1)^{+} \} \\ L_2= \{xy \mid x,y \in (a+b)^{*}, \mid x \mid=\mid y \mid, x \neq y \} \end{array}$ ... context- free but not regular and $L_2$ is context-free. Neither $L_1$ nor $L_2$ is context- free. $L_1$ context- free but $L_2$ is not context-free.

Consider the following languages.$$\begin{array}{ll} L_1= \{ wxyx \mid w,x,y \in (0+1)^{+} \} \\ L_2= \{xy \mid x,y \in (a+b)^{*}, \mid x \mid=\mid y \mid, x \neq y \} \e...

Arjun

18.3k views

Arjun asked Feb 12, 2020

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