# Recent activity by Praveen Saini

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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 $X_0$? $10(0^*+(10)^*)1$ $10(0^*+(10)^*)^*1$ $1(0+10)^*1$ $10(0+10)^*1 +110(0+10)^*1$
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Consider the following two statements: If all states of an NFA are accepting states then the language accepted by the NFA is $\Sigma_{}^{*}$. There exists a regular language $A$ such that for all languages $B$, $A \cap B$ is regular. Which one of the following is CORRECT? Only I is true Only II is true Both I and II are true Both I and II are false
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Consider the languages $L_1 = \phi$ and $L_2 = \{a\}$. Which one of the following represents $L_1 {L_2}^* \cup {L_1}^*$ ? $\{\epsilon\}$ $\phi$ $a^*$ $\{\epsilon, a\}$
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Minimum No of Gates NAND/NOR Ex-OR Ex-Nor Half Adder Half Subtractor Full Adder Full Subtractor NAND ? ? ? ? ? ? NOR ? ? ? ? ? ?
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We can say there are four types of strings in the language so the regex will be: a(a+b)+a + b(a+b)+b + a(a+b)+b + b(a+b)+a Please expleain where I am wrong
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$f(x) = 1 - |x - 1|$ $f(x) =1 + |x - 1|$ $f(x) = 2 - |x - 1|$ $f(x) = 2 + |x - 1|$
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Consider the machine $M$: The language recognized by $M$ is: $\left\{ w \in \{a, b\}^* \text{ | every a in$w$is followed by exactly two$b$'s} \right\}$ $\left\{w \in \{a, b\}^* \text{ | every a in$w$is followed by at least two$b$'s} \right\}$ ... $contains the substring$abb$'} \right\}$ $\left\{w \in \{a, b\}^* \text{ |$w$does not contain$aa$' as a substring} \right\}$
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A sequential circuit takes an input stream of 0's and 1's and produces an output stream of 0's and 1's. Initially it replicates the input on its output until two consecutive 0's are encountered on the input. From then onward, it produces an output stream, which is ... to be used to design the circuit. Give the minimized sum-of-product expression for J and K inputs of one of its state flip-flops
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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?
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This is from the first chapter questions of Sipser's book on TOC. I am stuck in some of the questions where we are asked to find the pumping length of the following languages. Find the minimum pumping length of the following regular languages:- L=$0^*1^+0^+1^* \cup \ 10^*1$ L=001 U 0*1* L=0*1* L=10 (11* 0)* 0 L= &#8714;
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Note : the bubbles are NOT gates
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Three of the five students are allocated to a hostel put in special requests to the warden, Given the floor plan of the vacant rooms, select the allocation plan that will accommodate all their requests. Request by X: Due to pollen allergy, I want to avoid a wing next to ... by Z: I believe in Vaastu and so I want to stay in South-West wing. The shaded rooms are already occupied. WR is washroom
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I tried it through state elimination method but I am getting stucked at the outgoing edge from D to A .
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find min no of states in dfa that accepts string begining or ending with 00 or 11
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Consider the circuit given below with initial state $Q_0=1, Q_1=Q_2=0$. The state of the circuit is given by the value $4Q_2+2Q_1+Q_0$ Which one of the following is correct state sequence of the circuit? $1, 3, 4, 6, 7, 5, 2$ $1, 2, 5, 3, 7, 6, 4$ $1, 2, 7, 3, 5, 6, 4$ $1, 6, 5, 7, 2, 3, 4$
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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 $00$.
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Is this language regular? L1:{wxwR&#8739;w,x&isin;{a,b}&lowast; and |w|,|x|>0}, wR is the reverse of string w Please explain..
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The number of states in the minimum sized DFA that accepts the language defined by the regular expression. $(0+1)^{*} (0+1) (0+1)^{*}$ is ________.
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A finite state machine with the following state table has a single input $x$ and a single out $z$ ... $01$ $10$ $101$ $110$
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The length of the shortest string NOT in the language (over $\Sigma = \{a, b\})$ of the following regular expression is _______. $a^*b^*(ba)^*a^*$
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Consider the circuit above. Which one of the following options correctly represents $f\left(x,y,z\right)$ $x\bar{z}+xy+\bar{y}z$ $x\bar{z}+xy+\overline{yz}$ $xz+xy+\overline{yz}$ $xz+x\bar{y}+\bar{y}z$
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Which of the following set can be recognized by a Deterministic Finite state Automaton? The numbers $1, 2, 4, 8, \dots 2^n, \dots$ written in binary The numbers $1, 2, 4, 8,\dots 2^n, \dots$ written in unary The set of binary string in which the number of zeros is the same as the number of ones. The set $\{1, 101, 11011, 1110111, \dots\}$
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Let $M=(\{q_0, q_1\}, \{0, 1\}, \{z_0, X\}, \delta, q_0, z_0, \phi)$ be a Pushdown automation where $\delta$ is given by $\delta(q_0, 1, z_0) = \{(q_0, Xz_0)\}$ $\delta(q_0, \epsilon, z_0) = \{(q_0, \epsilon)\}$ ... $\delta(q_0, 0, z_0) = \{(q_0, z_0)\}$ What is the language accepted by this PDA by empty stack? Describe informally the working of the PDA
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Let $L$ denote the languages generated by the grammar $S \to 0S0 \mid 00$. Which of the following is TRUE? $L = 0^+$ $L$ is regular but not $0^+$ $L$ is context free but not regular $L$ is not context free
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Consider the finite automaton in the following figure: What is the set of reachable states for the input string $0011$? $\{q_0,q_1,q_2\}$ $\{q_0,q_1\}$ $\{q_0,q_1,q_2,q_3\}$ $\{q_3\}$
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Let $L$ be the set of all binary strings whose last two symbols are the same. The number of states in the minimal state deterministic finite state automaton accepting $L$ is $2$ $5$ $8$ $3$
The complement of the language $L$ containing an equal number of $a's$,$b's$ and $c's$ is (a) regular (b) context free (c) context sensitive but not context free (d) recursive and not a cfl.
Consider the following three statements: Intersection of infinitely many regular languages must be regular. Every subset of a regular language is regular. If $L$ is regular and $M$ is not regular then $L ∙ M$ is necessarily not regular. Which of the following gives the correct true/ ... of the above? true, false, true. false, false, true. true, false, true. false, false, false. true, true, true.
Given the following state table of an FSM with two states $A$ and $B$ ... is the minimum length of an input string which will take the machine to the state $A=0,B=1$ with $output=1$. $3$ $4$ $5$ $6$
A control algorithm is implemented by the NAND – gate circuitry given in figure below, where $A$ and $B$ are state variable implemented by $D$ flip-flops, and $P$ is control input. Develop the state transition table for this controller.