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

# Recent questions in Theory of Computation

1
Which of the following is not a monotonically increasing grammar? (A) Context-sensitive grammar (B) Unrestricted grammar (C) Regular grammar (D) Context-free grammar
1 vote
2
Which of the following regular expressions denotes a language comprising all possible strings over the alphabet $\{a,b\}$? $a^*b^*$ $(a\mid b)^*$ $(ab)^+$ $(a\mid b^*)$
1 vote
3
Regarding power of recognition of language, which of the following statements is false? Non deterministic finite-state automata are equivalent to deterministic finite-state automata. Non-deterministic push-down automata are equivalent to deterministic push-down ... are equivalent to deterministic push-down automata. Multi-tape Turing Machines are equivalent to Single-tape Turing Machines.
1 vote
4
If $L_1$ and $L_2$ are context free language and $R$ a regular set, then which one of the languages below is not necessarily a context free language? $L_1L_2$ $L_1\cap L_2$ $L_1\cap R$ $L_1\cup L_2$
1 vote
5
If $L$ be a language recognizable by a finite automaton, then language from $\{L\} = \{w$ such that $w$ is a prefix of $v$ where $v\in L\}$, is a regular language. context-free language. context-sensitive language. recursive enumeration language
6
Which of the following statements is correct? $A=\{a^nb^n\mid n= 0,1,2,3\dots \}$ is regular language Set $B$ of all strings of equal number of $a$'s and $b$'s defines a regular language $L(A^*B^*) \cap B$ gives the set $A$ None of these.
7
The CFG $S \to aS\mid bS\mid a\mid b$ is equivalent to $(a+b)$ $(a+b)(a+b)^*$ $(a+b)(a+b)$ all of these
1 vote
8
Palindromes can't be recognized by any Finite State Automata because: FSA cannot remember arbitrarily large amount of information. FSA cannot deterministically fix the midpoint. Even if the mid-Point is known an FSA cannot find whether the second half of the string matches the first half. All of the above.
1 vote
9
If $L1$ is CFL and $L2$ is regular language which of the following is false? $L1-L2$ is not Context free $L1$ intersection $L2$ is Context free $\sim L1$ is Context free Both (A) and (C)
10
Which of the following is wrong? Turing machine is a simple mathematical model of general purpose computer Turing machine is more powerful than finite automata Turing Machine can be simulated by a general purpose computer All of these
11
Given two DFA's $M1$ and $M2$. They are equivalent if $M1$ and $M2$ has the same number of states $M1$ and $M2$ accepts the same language i.e $L(M1)=L(M2)$ $M1$ and $M2$ has the same number of final states None of the above
12
What is the complement of the language accepted by the NFA shown below? $\not{O}$ $\{\epsilon\}$ $a^*$ $\{a,\epsilon\}$ $1$ $2$ $3$ $4$
13
Let $L$ be a language and $L’$ be its complement. Which one of the following is NOT a viable possibility? Neither $L$ nor $L’$ is RE. One of the $L$ and $L’$ is RE but not recursive;the other is not RE. Both $L$ and $L’$ are RE but not recursive. Both $L$ and $L’$ are recursive.
14
Let $L1$ be a recursive language, and let $L2$ be a recursively enumerable but not recursive language. Which one of the following is TRUE? $L1’$ is recursive and $L2’$is recursively enumerable. $L1’$ is recursive and $L2’$is not recursively enumerable. $L1’$ and $L2’$is recursively enumerable. $L1’$ is recursively enumerable and $L2’$is recursive.
15
According to the given language, which among the following expressions does it correspond to ? Language $L=\{x\in\{0,1\}\mid x\text{ is of length 4 or less}\}$. $(0+1+0+1+0+1+0+1)^4$ $(0+1)^4$ $(01)^4$ $(0+1+\varepsilon)^4$
16
Let $G$ be a grammar in CFG and let $W_1,W_2\in L(G)$ such that $\mid W_1\mid=\mid W_2\mid$ then which of the following statements is true? Any derivation of $W_1$ has exactly the same number of steps as any derivation of $W_2$. Different derivation have different length. Some derivation of $W_1$ may be shorter than the derivation of $W_2$ None of the options
17
A regular expression is $(a+b^{\ast}c)$ is equivalent to set of strings with either $a$ or one or more occurrence of $b$ followed by $c$. $(b^{\ast}c+a)$ set of strings with either $a$ or zero or more occurrence of $b$ followed by $c$. Both (B) and (C)
Which of the following are undecidable? $P1$: The language generated by some CFG contains any words of length less than some given number $n$. $P2$: Let $L1$ be CFL and $L2$ be regular, to determine whether $L1$ and $L2$ have common elements $P3$: Any given CFG is ambiguous or not. ... CFG $G$, to determine whether epsilon belongs to $L(G)$ $P2$ only $P1$ and $P2$ only $P2$ and $P3$ only $P3$ only
What is the meaning of regular expression $\Sigma^*001\Sigma^*$? Any string containing ‘$1$’ as substring Any string containing ‘$01$’ as substring Any string containing ‘$011$’ as substring All string containing ‘$001$’ as substring