search
Log In

Web Page

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

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

Most answered questions in Theory of Computation

51 votes
14 answers
1
What is the complement of the language accepted by the NFA shown below? Assume $\Sigma = \{a\}$ and $\epsilon$ is the empty string. $\phi$ $\{\epsilon\}$ $a^*$ $\{a , \epsilon\}$
asked Aug 5, 2014 in Theory of Computation gatecse 9.3k views
34 votes
11 answers
2
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 ___________ .
asked Feb 14, 2017 in Theory of Computation Arjun 12.2k views
51 votes
11 answers
3
42 votes
11 answers
4
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. $X_0 = 1 X_1$ $X_1 = 0 X_1 + 1 X_2$ ... in $X_0$? $10(0^*+(10)^*)1$ $10(0^*+(10)^*)^*1$ $1(0+10)^*1$ $10(0+10)^*1 +110(0+10)^*1$
asked Feb 12, 2015 in Theory of Computation jothee 8k views
33 votes
10 answers
5
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
asked Feb 14, 2018 in Theory of Computation gatecse 9.4k views
51 votes
10 answers
6
Let $\delta$ denote the transition function and $\widehat{\delta}$ denote the extended transition function of the $\epsilon$-NFA whose transition table is given below: $\begin{array}{|c|c|c|c|}\hline \delta & \text{$\epsilon$} & \text{$a$} & \text{$ ... $\widehat{\delta}(q_2, aba)$ is $\emptyset$ $\{q_0, q_1, q_3\}$ $\{q_0, q_1, q_2\}$ $\{q_0, q_2, q_3 \}$
asked Feb 14, 2017 in Theory of Computation Arjun 11.4k views
20 votes
10 answers
7
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 \}$ $\{a^mb^n \mid m > n, n \geq 0 \}$ $\{a^mb^n \mid m > n, n > 0 \}$
asked Feb 14, 2017 in Theory of Computation khushtak 7.6k views
35 votes
10 answers
8
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 ______________ .
asked Feb 14, 2017 in Theory of Computation Madhav 6.8k views
54 votes
10 answers
9
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 $L$? $(0^*10^*1)^*$ $0^*(10^*10^*)^*$ $0^*(10^*1)^*0^*$ $0^*1(10^*1)^*10^*$
asked Sep 30, 2014 in Theory of Computation jothee 10.8k views
45 votes
10 answers
10
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
asked Sep 16, 2014 in Theory of Computation Kathleen 8.1k views
44 votes
9 answers
11
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 $G_2$ ... $\{ a^mb^n \mid m \geq 0 \text{ and } n >0\}$ and $\{ a^mb^n \mid m > 0 \text{ or } n>0\}$
asked Feb 12, 2016 in Theory of Computation Sandeep Singh 11.8k views
24 votes
9 answers
12
In some programming language, an identifier is permitted to be a letter followed by any number of letters or digits. If $L$ and $D$ denote the sets of letters and digits respectively, which of the following expressions defines an identifier? $(L + D)^+$ $(L.D)^*$ $L(L + D)^*$ $L(L.D)^*$
asked Oct 8, 2014 in Theory of Computation Kathleen 6.3k views
38 votes
9 answers
13
Match the following NFAs with the regular expressions they correspond to: P Q R S $\epsilon + 0\left(01^*1+00\right)^*01^*$ $\epsilon + 0\left(10^*1+00\right)^*0$ $\epsilon + 0\left(10^*1+10\right)^*1$ $\epsilon + 0\left(10^*1+10\right)^*10^*$ $P-2, Q-1, R-3, S-4$ $P-1, Q-3, R-2, S-4$ $P-1, Q-2, R-3, S-4$ $P-3, Q-2, R-1, S-4$
asked Sep 12, 2014 in Theory of Computation Kathleen 6.3k views
38 votes
8 answers
14
Consider the context-free grammars over the alphabet $\left \{ a, b, c \right \}$ given below. $S$ and $T$ are non-terminals. $G_{1}:S\rightarrow aSb \mid T, T \rightarrow cT \mid \epsilon$ $G_{2}:S\rightarrow bSa \mid T, T \rightarrow cT \mid \epsilon$ The language $L\left ( G_{1} \right )\cap L(G_{2})$ is Finite Not finite but regular Context-Free but not regular Recursive but not context-free
asked Feb 14, 2017 in Theory of Computation Arjun 6.4k views
17 votes
8 answers
15
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
asked Jul 4, 2016 in Theory of Computation Anu 8.4k views
5 votes
8 answers
16
Let $M$ range over Turing machine descriptions, Consider the set $\text{REG = {M | L(M) is a regular set }}$ and let the complement of $REG$ be $Co-REG.$ Which of the following is true? REG is recursively enumerable but Co-REG is not REG is not recursively enumerable but Co-REG is Both are recursively enumerable. None of the above
asked Nov 18, 2014 in Theory of Computation Isha Karn 1.1k views
37 votes
8 answers
17
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 $L(M)$? $aaa$ $aabab$ $baaba$ $bab$
asked Nov 2, 2014 in Theory of Computation Ishrat Jahan 10.6k views
31 votes
8 answers
18
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 $00$.
asked Sep 22, 2014 in Theory of Computation Kathleen 7.1k views
24 votes
8 answers
19
$S \to aSa \mid bSb\mid a\mid b$ 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
asked Sep 22, 2014 in Theory of Computation Kathleen 9.2k views
66 votes
8 answers
20
Consider the regular language $L=(111+11111)^{*}.$ The minimum number of states in any DFA accepting this languages is: $3$ $5$ $8$ $9$
asked Sep 22, 2014 in Theory of Computation Rucha Shelke 13.7k views
...