Example:- Consider the following table of a system: Process Allocated Мах Available R1 R2 R3 R4 R1 R2 R3 R4 R1 | R2 | R3 R4 P1 1 2 1 2 P2 2 2 7 5 2 1 P3 3 6 5 6. P4 2 3 4 4 3 5 P5 3 3 6. · Compute NEED Matrix. . Is the system in safe state? Justify. 2. 2. in
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- Consider the following loop: //Precondition: (index=x) ^ (x 2 1) ^ (y=0) while (index >1) { index = index/2; ++y; } //Postcondition: (index =1) ^ (2° < x) ^ (x<2♥+1) Suppose we have already proved the first two parts of the postcondition, that is, (index = 1) and (2Y < x). Now we are trying to prove %D the last part (x < 2y+1). If (x < 2Y+1 index) is a loop invariant, can it be used to prove (x < 2Y+1)? Explain why or why not. Yes. Because the statement (x < 2y+1 index) is true before and after loop execution. O Yes. Because it is given that (r<2+1*index) is an invariant, and (x<2+1xindex) is equivalent to (r<2+1). O No. Since index = 1, the two sides of the proof would be the same which means there is nothing to prove. Yes. Because when the loop terminates we have (index=1), so x < 2y+1index = 2y+1Consider the following truth table, which includes don't cares: ABC 0 0 0 0 0 1 O O O 1 1 100 1 0 1 1 11 1 1 0 1 1 R 1 1 X X O 0 1 X Draw a Karnaugh Map corresponding to this truth table, where R is the output. Draw boxes around the appropriate bits, following the appropriate rules for doing so. For full credit, you must draw boxes in a way that guarantees that both the number of products and the number of sums is minimized. In addition, write out the optimized sum-of-products equation corresponding to the boxes you drew.Type in Latex **Problem**. Let $$A = \begin{bmatrix} .5 & .2 & .3 \\ .3 & .8 & .3 \\ .2 & 0 & .4 \end{bmatrix}.$$ This matrix is an example of a **stochastic matrix**: its column sums are all equal to 1. The vectors $$\mathbf{v}_1 = \begin{bmatrix} .3 \\ .6 \\ .1 \end{bmatrix}, \mathbf{v}_2 = \begin{bmatrix} 1 \\ -3 \\ 2 \end{bmatrix}, \mathbf{v}_3 = \begin{bmatrix} -1 \\ 0 \\ 1\end{bmatrix}$$ are all eigenvectors of $A$. * Compute $\left[\begin{array}{rrr} 1 & 1 & 1 \end{array}\right]\cdot\mathbf{x}_0$ and deduce that $c_1 = 1$.* Finally, let $\mathbf{x}_k = A^k \mathbf{x}_0$. Show that $\mathbf{x}_k \longrightarrow \mathbf{v}_1$ as $k$ goes to infinity. (The vector $\mathbf{v}_1$ is called a **steady-state vector** for $A.$) **Solution**. To prove that $c_1 = 1$, we first left-multiply both sides of the above equation by $[1 \, 1\, 1]$ and then simplify both sides:$$\begin{aligned}[1 \, 1\, 1]\mathbf{x}_0 &= [1 \, 1\, 1](c_1\mathbf{v}_1 +…
- Consider the following table of a system: Process Allocated Мах Available R1 R2 R3 R4 R1 R2 R3 2 1 R4 R1 R2 R3 R4 P1 2 2 P2 2 3 3 3 3 3 5 9 00 2 P3 3 4 4 P4 2 4 2 3 6 5 P5 1 3 2 2 2 3 3 c. Compute NEED Matrix. d. Is the system in safe state? Justify 3. 3. 2.All businesses want to keep their customers happy. To do that, many companies assign a certain amount of time to each customer to optimize the business. The alternative would be to hire more employees, which would lead to higher costs. This problem requires you to simulate how authorities optimize the number of cashiers at the entrance of a toll bridge to make sure drivers are satisfied. Make the following assumptions: There is one cashier per line. The line works as a queue with no cars cutting the line or leaving it. One car arrives at the entrance every 10 seconds. It takes 90 seconds (1.5 minutes) to process the payment, starting from the moment a cashier is available. Assume there is no pause between cars. Your Tasks: Design class CarInLine, with the following specifications: The class has two instance variables: arrivalTime and DepartureTime, stored as integers. Define a constructor that accepts an integer as an argument representing the arrival time, in which you set…Consider the following snapshot of a system: Allocation Мах АВCD АВCD Po P1 P2 P3 P4 3014 5117 2210 3211 3121 3321 0510 4612 4212 6325 Using the banker's algorithm, determine whether or not each of the following states is unsafe. If the state is safe, illustrate the order in which the processes may complete. Otherwise, illustrate why the state is unsafe. а. Available 3D (0, 3, 0, 1) b. Available = (1, 0, 0, 2) If a request from process P3 arrives for (3, 0, 2, 0), can the request be granted immediately?
- All businesses want to keep their customers happy. To do that, many companies assign a certain amount of time to each customer to optimize the business. The alternative would be to hire more employees, which would lead to higher costs. This problem requires you to simulate how authorities optimize the number of cashiers at the entrance of a toll bridge to make sure drivers are satisfied. Make the following assumptions: There is one cashier per line. The line works as a queue with no cars cutting the line or leaving it. One car arrives at the entrance every 10 seconds. It takes 90 seconds (1.5 minutes) to process the payment, starting from the moment a cashier is available. Assume there is no pause between cars. Written in java, Your Tasks: Design class CarInLine, with the following specifications: The class has two instance variables: arrivalTime and DepartureTime, stored as integers. Define a constructor that accepts an integer as an argument representing the arrival time, in…This question is answered but I think there are some problems in the answer. It says that n^(1/3) < n^(1/logn) and (3/2)^n < 2^logn but I guess they both are supposed to be inversed. Since n^(1/logn) has the same value for every n, it is constant and it does not supposed to have a growth rate since it is zero. Can you control and correct every part of the solution? The solution link is here: https://www.bartleby.com/questions-and-answers/order-the-following-functions-in-increasing-order-of-growth-rate-i.e.-o.-classes.-log-n-log-log-n-n-/b85a39f1-017d-4c04-8553-4d01341429f8Consider the first round of DES. Let us assume that the round key K, is the vector of all ones and we have the following input to the encryption round: X = Lo || Ro, where Lo vector (i.e., 32 zeros). = 1011 0100 1000 1101 1010 0100 1110 0101 and R, is the all-zero What would be the output of the first round of encryption? Show your work for each step (output of expansion box, the S-boxes, and the permutation inside the f-function).
- Suppose a 2D bounding box is given by (≤ is "less than or equal to"): -1 ≤ x ≤ 1-10 ≤ y ≤ 10 Compute the new Bounding Box for the transformation given by the following matrix: (see section 9.4.4) 0.866 -0.5 0.5 0.866 Now enter the xmax for the new Bounding Box (round it to 3 decimal places, if needed).The following table represents the present state of a system. Process Allocated Маx Available R1 R2 R3 R4 R1 R2 R3 R4 R1 R2 R3 R4 P1 4 2 2 P2 1 2 2 3 P3 1 1 1. Compute Need Matrix 2. Use Bankers algorithm to test if the system is in safe state or not. 3. Write the safe Sequence. 2. 1. 3.Question 1 Suppose that M is a dfa and that M = ({90, 91, 92}, {0,1}, 6, 90, {91}) where 8 = {((90, 0), 90), ((90, 1), 91), ((91,0), 90), ((91, 1), 92), ((92, 0), 92), ((92, 1), 91)}. S* (90, X) None of the other answers is correct. 90 92 = 91