Dark Mode

Recent questions and answers in Theory of Computation

1 vote

3 answers

1

GATE CSE 2024 | Set 2 | Question: 52
Let $L_{1}$ be the language represented by the regular expression $b^{*} a b^{*}\left(a b^{*} a b^{*}\right)^{*}$ and $L_{2}=\left\{w \in(a+b)^{*}|| w \mid \leq 4\right\}$, where $|w|$ denotes the length of string $w$. The number of strings in $L_{2}$ which are also in $L_{1}$ is _________.

Mihir L. Agrawal answered in Theory of Computation Mar 23

by Mihir L. Agrawal

1.7k views

0 votes

0 answers

2

THEORY OF AUTOMATA ASSIGNMENT # 1 1. Write regular expressions and draw NFA for the following languages over the alphabet Σ = {a, b}: a. All strings that do not end with aa. b. All strings that contain an even number of b’s c. All strings that contain atleast two a’s or exactly two b’s d. All strings that ends with double letters (aa or bb) e. All strings that does not ends with double letter.(can end with ab or ba)

Talha Riaz asked in Theory of Computation Mar 23

24 views

0 votes

1 answer

3

Set of binary strings starting with 11 and ending with 00. E.g., 1100,1110100 ,1100100

prasantkr.singh answered in Theory of Computation Mar 22

by prasantkr.singh

42 views

1 vote

2 answers

4

GATE CSE 2024 | Set 2 | Question: 31
Let $\text{M}$ be the $5$-state $\text{NFA}$ with $\epsilon$-transitions shown in the diagram below. Which one of the following regular expressions represents the language accepted by $\text{M}$? $(00)^{*}+1(11)^{*}$ $0^{*}+\left(1+0(00)^{*}\right)(11)^{*}$ $(00)^{*}+\left(1+(00)^{*}\right)(11)^{*}$ $0^{+}+1(11)^{*}+0(11)^{*}$

ashwinsuthar1 answered in Theory of Computation Mar 19

by ashwinsuthar1

2.0k views

0 votes

1 answer

5

Write regular expression for the set of strings of 0's and 1's with at most one pair of consecutive 1's.

Mrityudoot answered in Theory of Computation Mar 16

63 views

0 votes

0 answers

6

Hopcroft, Ullman Theorem 9.7 Reductions
There exists a language Ld = {M | M doesn't belong to L(M)}. Ld is the collection of Turing machines (programs) M such that M does not halt and accept when given itself as input. It is known and proved that Ld is a non- ... and Ld is non-RE, ATM must be non-RE. But we know that ATM is Recursively Enumerable and undecidable. How is this possible?

dopq12 asked in Theory of Computation Mar 5

by dopq12

75 views

2 votes

3 answers

7

GATE CSE 2024 | Set 1 | Question: 51
Consider the following two regular expressions over the alphabet $\{0,1\}$ : $r= 0^{*}+1^{*}$ $s = 01^{*} + 10^{*}$ The total number of strings of length less than or equal to $5$, which are neither in $r$ nor in $s$, is ________.

jvishal answered in Theory of Computation Mar 2

1.5k views

0 votes

2 answers

8

#Convert the NFA in to equivalent R.E.

m1_lan____ answered in Theory of Computation Feb 26

142 views

0 votes

0 answers

9

Çșȇ ʛấẗẻ asked in Theory of Computation Feb 24

by Çșȇ ʛấẗẻ

79 views

0 votes

0 answers

10

Consider a regular language R and a context free language C. Let the PDA that recognizes C be called P=(QP,∑,Γ,δP,q0P,FP), and the DFA that reconginzes R be (QR,∑,δR,q0R,FR).

Vedantthakkar asked in Theory of Computation Feb 24

by Vedantthakkar

118 views

0 votes

0 answers

11

Pumping Lemma
Use the Pumping Lemma to show that the following languages over Σ={�,�}Σ={a,b} are not regular. In each case, carefully describe the string that will be pumped and explain why pumping it leads to a contradiction. {aaabnan∣n≥0} {ww∣w∈Σ∗}

jg662 asked in Theory of Computation Feb 22

by jg662

71 views

2 votes

1 answer

12

GATE CSE 2024 | Set 2 | Question: 42
Consider a context-free grammar $\text{G}$ with the following $3$ rules. \[ S \rightarrow a S, S \rightarrow a S b S , S \rightarrow c \] Let $w \in L(G)$. Let $ n_{a}(w), n_{b}(w), n_{c}(w) $ denote the number of times $a, b, c$ occur in $w$, respectively. Which of ... $n_{a}(w)>n_{c}(w)-2$ $n_{c}(w)=n_{b}(w)+1$ $n_{c}(w)=n_{b}(w) * 2$

liontig37 answered in Theory of Computation Feb 22

1.6k views

0 votes

0 answers

13

Prove that the following languages are not regular. You may use the pumping lemma and the closure of the class of regular languages under union, intersection, and complement. a. {0"1"0"| m, n 2 0} b. (0"1"| m ‡ n) c. (w| w € {0,1)* is not a palindrome) d. (wtw| w,t € (0,1)*)

krishan_rathi asked in Theory of Computation Feb 21

by krishan_rathi

111 views

0 votes

1 answer

14

GATE CSE 2024 | Set 1 | Question: 40
Consider the $5$ -state $\text{DFA}$. $M$ accepting the language $L(M) \subset(0+1)^{*}$ shown below. For any string $w \in(0+1)^*$ let $n_0(w)$ be the number of $0^{\prime} s$ in $w$ and $n_1(w)$ be the number of 1 's in $w$. ... $4$ are distinguishable in $M$ States $2$ and $5$ are distinguishable in $M$ Any string $w$ with $n_0(w)=n_1(w)$ is in $L(M)$

phaniphani answered in Theory of Computation Feb 16

2.2k views

0 votes

1 answer

15

GATE CSE 2024 | Set 1 | Question: 13
Let $L_1, L_2$ be two regular languages and $L_3$ a language which is not regular. Which of the following statements is/are always TRUE? $L_1=L_2$ if and only if $L_1 \cap \overline{L_2}=\phi$ $L_1 \cup L_3$ is not regular $\overline{L_3}$ is not regular $\overline{L_1} \cup \overline{L_2}$ is regular

malaviya_parth answered in Theory of Computation Feb 16

by malaviya_parth

2.5k views

2 votes

2 answers

16

GATE CSE 2024 | Set 2 | Question: 12
Which one of the following regular expressions is equivalent to the language accepted by the $\text{DFA}$ given below? $0^{*} 1\left(0+10^{*} 1\right)^{*}$ $0^{*}\left(10^{*} 11\right)^{*} 0^{*}$ $0^{*} 1\left(010^{*} 1\right)^{*} 0^{*}$ $0\left(1+0^{*} 10^{*} 1\right)^{*} 0^{*}$

Deepak Poonia answered in Theory of Computation Feb 16

by Deepak Poonia

2.2k views

0 votes

1 answer

17

Not Regular language [find out]
Why is C is regular as it non regular as? Please help me with this confusion

bluesta answered in Theory of Computation Feb 15

214 views

0 votes

1 answer

18

Give state diagrams of DFAs recognizing the following languages. In all parts, the alphabet is {0,1}.{w| w starts with 0 and has odd length, or starts with 1 and has even length}

Sujith48 answered in Theory of Computation Feb 15

101 views

0 votes

0 answers

19

Each of the following languages is the complement of a simpler language. In each part, construct a DFA for the simpler language, then use it to give the state diagram of a DFA for the language given. In all parts, Σ = {a, b}.{w| w does not contain the substring ab} {w| w does not contain the substring baba} {w| w contains neither the substrings ab nor ba} {w| w is any string not in a∗ ∪ b∗ } ( ∪ is the union )

rania asked in Theory of Computation Feb 14

by rania

104 views

0 votes

3 answers

20

michael sipser chp 1, 3rd edition, Q 12 , dfa
let D= {w | w contains an even no. of a's and an odd no. of b's and does not contain the substring ab } give a DFA with Five states that recognizes D and a regular expression that generates D.

cherry348 answered in Theory of Computation Feb 12

3.6k views

3 votes

1 answer

21

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 32
Which of the following sets has the greatest cardinality? The set of real numbers R The set of all functions from R to {0,1} The set of all finite subsets of natural numbers The set of all finite-length binary strings

Bharadwaja1557 answered in Theory of Computation Feb 7

by Bharadwaja1557

404 views

5 votes

1 answer

22

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 64
Which of the following languages are Turing-recognizable? A. $\{\langle M\rangle \mid M$ is a (deterministic) Turing machine and $M$ accepts 010$\}$. B. $\{\langle M\rangle \mid M$ is a nondeterministic Turing machine and $M$ accepts 010 ... $\left\{\langle M\rangle \mid M\right.$ is a Turing machine and $\left.L(M)=\Sigma^*\right\}$.

Prabhas answered in Theory of Computation Feb 6

442 views

3 votes

1 answer

23

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 35
Which of the following strings are a member of the language described by the regular expression $\left(a^* {b} {a}^* b a^* b {a}^*\right)^*$ $b b b b$ $bbaaabb$ $bbaaabbbabb$ $b b a b b b a b$

shubhsy1729 answered in Theory of Computation Feb 6

522 views

4 votes

0 answers

24

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 31
DeMorgan's Laws ensure that Closure under intersection and complementation imply closure under union. Closure under intersection and union imply closure under complementation. Closure under union and complementation imply closure ... Closure under any two of union, intersection, and complementation implies closure under all three.

GO Classes asked in Theory of Computation Feb 5

306 views

4 votes

0 answers

25

GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 65
Which of the following statements are true for every language $\mathrm{L} \subseteq\{0,1\}^*?$ $L^{\star}$ is infinite. $L$ is accepted by some DFA if and only if $L$ is accepted by some NFA. If $\mathrm{L}$ is the ... $\mathrm{L}$ is undecidable. If $\mathrm{L}$ is the union of two decidable languages, then $\mathrm{L}$ is decidable.

GO Classes asked in Theory of Computation Feb 5

575 views

53 votes

3 answers

26

GATE CSE 2006 | Question: 30
For $s\in (0+1)^{*}$ let $d(s)$ denote the decimal value of $s ($e.g. $d (101) = 5 ).$ Let $L=\left \{ s\in (0+1)^*\mid d(s) \text{ mod } 5=2 \text{ and }d(s) \text{ mod } 7\neq 4 \right \}$Which ... following statements is true? $L$ is recursively enumerable, but not recursive $L$ is recursive, but not context-free $L$ is context-free, but not regular $L$ is regular

Amoljadhav answered in Theory of Computation Feb 3

7.6k views

0 votes

1 answer

27

Why is L1 not DCFL?

Mrityudoot answered in Theory of Computation Jan 28

113 views

6 votes

1 answer

28

GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 23
Which of the following statements is/are false? If a context-free grammar $\mathrm{G}$ is in Chomsky's normal form, then $\mathrm{G}$ is not ambiguous. For every number $n$ ... s a $10$-state NFA that accepts $\text{L}$ then there's a $100$-state DFA that accepts $\mathrm{L}$.

GO Classes answered in Theory of Computation Jan 28

600 views

5 votes

1 answer

29

GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 24
Let $\mathrm{M}$ be a $8$-state Deterministic Finite Automaton over the alphabet $\{a, b, c\}$. If the language accepted by $\text{M}$ i.e. $\text{L(M)}$ is finite, then the maximum possible cardinality of $\text{L(M)}$ is __________.

GO Classes answered in Theory of Computation Jan 28

520 views

5 votes

1 answer

30

GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 55
Recall that a Turing machine $\text{T}$ can be represented or 'coded' by an integer $m$. Let us write 'the $m$ th Turing machine' to mean the Turing machine coded by $m$. Which of the following sets is not ... machine halts on the input $m$. The set of $n$ such that all Turing machines halt on the input $n$.

GO Classes answered in Theory of Computation Jan 28

468 views

7 votes

1 answer

31

GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 56
For a string $x=x_1 \cdots x_n \in \Sigma^*$, where $\Sigma$ is any alphabet and $x_1, \ldots, x_n \in \Sigma$, we write $x^{\uparrow m}=x^m$ (that is, the usual power of strings) and $x^{\downarrow m}=x_1^m \cdots x_n^m$. For empty ... $\left\{(a b c)^{\downarrow n} \mid n \geq 0\right\}$

GO Classes answered in Theory of Computation Jan 28

448 views

8 votes

1 answer

32

GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 57
Consider a pushdown automaton (PDA) with two control states $Q=\{q 1, q 2\}$, start state $q 1$, input alphabet $\Sigma=\{a, b\}$, stack alphabet $\Gamma=\{\perp, a\}$ (where $\perp$ is the start symbol ... $21$ accepted by the above pushdown automaton is _________.

GO Classes answered in Theory of Computation Jan 28

541 views

21 votes

5 answers

33

GATE CSE 2001 | Question: 2.6
Consider the following languages: $L1=\left\{ww \mid w \in \{a,b\}^*\right\}$ $L2=\left\{ww^R \mid w \in \{a,b\}^*, w^R \text{ is the reverse of w} \right\}$ $L3=\left\{0^{2i} \mid \text{ i is an integer} \right\}$ ... $L1$ and $L2$ Only $L2, L3$ and $L4$ Only $L3$ and $L4$ Only $L3$

bluesta answered in Theory of Computation Jan 28

8.0k views

1 vote

1 answer

34

Gate CSE Made Easy Test Series
Construct a minimal finite state automation that accepts the language over {0, 1} of all strings that contain neither the substring 00 nor the substring 11. What is the number of states in this machine? For this question when we draw the DFA there ... and NFA contains 3 states minimum. So according to question what shall be the answer for this question? 3 or 4? Why?

prasantkr.singh answered in Theory of Computation Jan 23

by prasantkr.singh

221 views

1 vote

1 answer

35

Is it DCFL or CFL?
If it’s DCFL then also construct the DPDA ?

yadavmayank742 answered in Theory of Computation Jan 21

by yadavmayank742

143 views

3 votes

2 answers

36

GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 44
Which of the following statements is/are false? Let $\text{A}$ and $\text{B}$ be sets of languages over some fixed alphabet $\Sigma$, with $\text{A} \subseteq \text{B}$. If $\text{A}$ is closed under some operation $\text{P},$ then ... $\mathrm{L} 2$ $\subseteq \mathrm{L} 1$, then $\mathrm{L} 2$ is decidable.)

raj_uddeshya157 answered in Theory of Computation Jan 21

by raj_uddeshya157

534 views

32 votes

3 answers

37

GATE CSE 2001 | Question: 7
Let a decision problem $X$ be defined as follows: $X$: Given a Turing machine $M$ over $\Sigma$ and any word $w \in \Sigma$, does $M$ loop forever on $w$? You may assume that the halting problem of Turing machine is undecidable but partially decidable. Show that $X$ is undecidable Show that $X$ is not even partially decidable

ajayraho answered in Theory of Computation Jan 21

4.6k views

3 votes

1 answer

38

GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 15
Consider the following NFA $M$ and say what language is recognised by constructing the machine that recognises the complement of $L(M)$ in $\{a\}^*$. $\emptyset$ $\{a\}^*$ $\{a\}$ $\{\varepsilon\}$

GO Classes answered in Theory of Computation Jan 21

435 views

2 votes

1 answer

39

GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 42
Consider the following context-free language: $L_1=\left\{a^m b^n c^n \mid n, m \geq 0\right\}$. Which of the following choices of language $L_2$ is context-free and ensures that $L_1 \cap L_2$ ... and $\left.m \geq 0\right\}$ $L_2=\left\{a^k b^{2 k} c^{2 k} \mid k \geq 0\right\}$

GO Classes answered in Theory of Computation Jan 21

500 views

8 votes

1 answer

40

GO Classes Test Series 2024 | Mock GATE | Test 12 | Question: 43
Let $\text{D}$ be a DFA with $n$ states $\& \;\text{N}$ be an NFA with $n$ states. Which of the following is/are true? If $\text{D}$ accepts some string of length $n$, then the language of $\text{D}$ is infinite ... $\mathrm{N}$ accepts some string of length $n-1$, then the language of $\mathrm{N}$ is infinite.

GO Classes answered in Theory of Computation Jan 21

637 views

To see more, click for all the questions in this category.

Recent questions and answers in Theory of Computation