Problem 2. ( Matloff) Consider the ALOHA example, but now assume that initially exactly one node is active. Suppose it is known that X₁ ‡ X₂. Find the probability that there were 0, 1 or 2 collisions during the next two epochs analytically and confirm via R simulation.
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- Use the Subset construction, as defined in the lecture notes, to construct DFA from the NFA produced by Thompson's construction on the regular expression x* ( y | € ) ( € | y) How many x-transitions (edges labelled x) does the DFA have? Choose... v How many accepting states does the DFA have? Choose... v How many states does the DFA have? Choose... How many y-transitions (edges labelled y) does the DFA have? Choose... v How many e-transitions (edges labelled € does the DFA have? Choose... vLet E = {a, b} and L = {ww|w e E* and w is of length k}. Show that for each k, no DFA can recognize Lk with fewer than 2k states.B. Suppose we wish to animate a bouncing ball. We are given keyframes for the ball's motion. The key frames are at times T = {0, 3, 9, 15} with associated height values of H = {1, 6, 8, 3}. 1. Plot the graph of height versus time using linear interpolation between key frames. 2. Since the ball's speed changes as it falls and as it bounces, linear interpolation will not give a realistic result. Which method would create the most realistic bounce? And how would the graph look like? H 16- 14- 12- 10- 8- 6- 4- 2- 0- →T 4 6 8. 10 12 14 16
- (1) Draw a transition graph for the dfa M={ Q,E, 8.q..F), where Q={g,.g1-42}. E= {a, b}, F = {q1} and ô is defined as S(q0, a) = q1- 8(q0, b) = q0, 8(q1, b) = q1. 8(q1, a) = q2, 8(q2, b) = q2, ô(q2, a) = q2 (2) Give the language accepted by the above dfa.Consider two cooperating processes P5 and P6. Suppose that, at any time, P6 want toenter its critical section. Write an algorithm using Peterson’s solution which shows thatP6 can finally enter into its criticalsection. Consider the turn value for P5 to be 10 andP6 to be 12.-With respect to the performance model, it should be implemented efficiently. Your answer Ring the network in a ring topology comes back around to the first node, creating a complete circuit. to a bus network, rings have nodes daisy chained, but the end of Your answer ----This part includes defining the problem, designing the corresponding model, and devising a set of experiments for the formulated simulation model.
- Q3: Using Mealy model only, develop the state-diagrams for: A. A sequential network has one input and one output that detect sequences 001 and 10110. B. A sequential network has one input and one output. When the input sequence 01101 occurs, the output becomes 1 and remains 1 until the sequence 01101 occurs again in which case the output returns to 0. The output then remains 0 until 01101 occurs a third time, etc.Let (X, Y) - Uniform(D) with DC R2 being a disc contered at the point (a, b) (s00 the Figure below). Dofine V(x-a)2 +(Y-6)2 Out of the four random variables X, Y,0, R. find a pair which Y-by = arctan and R is independent. (,4) O (X,Y) O (X, R) O (X, e) O (R,Y) o (e,Y) O (R,e) 1. Out of the four random variables X,Y, R, 0. find a pair which is independent. True O False 2. The random variables X, Y aro uncorrolatod.Assume for an undirected graph with 6 vertices and 6 edges that a vertex index requires 3 bytes, a pointer requires 5 bytes, and that edge weights require 3 bytes. Since the graph is undirected, each undirected edge is represented by two directed edges. Calculate the byte requirements for an adjacency matrix.
- From the chart, estimate (roughly) the number of transistors per IC in 2016. Using your estimate and Moore's Law, what would you predict the number of transistors per IC to be in 2040? In some applications, the variable being studied increases so quickly ("exponentially") that a regular graph isn't informative. There, a regular graph would show data close to 0 and then a sudden spike at the very end. Instead, for these applications, we often use logarithmic scales. We replace the y-axis tick marks of 1, 2, 3, 4, etc. with y-axis tick marks of 101 = 10, 102 = 100, 103 = 1000, 104 = 10000, etc. In other words, the logarithms of the new tick marks are equally spaced. Technology is one area where progress is extraordinarily rapid. Moore's Law states that the progress of technology (measured in different ways) doubles every 2 years. A common example counts the number of transitors per integrated circuit. A regular y-axis scale is appropriate when a trend is linear, i.e. 100…In the Erdös-Rényi random network model, suppose N=101 and p=1/20, that is, there are 101 vertices, and every pair of vertices has a probability of 1/20 of being connected by an edge. For the network model given what is the probability that a network generated with those parameters has exactly 400 edges? No need to give the decimal value, the mathematical expression will sufficeQuestion 1 Refer to the following network flow and state the min cut, of the graph G. S 3/7 6/6 -5/5 (s,v1),(s,v3),(s,v2) 1/1 (v1,v4), (v1,v3),(s,v3),(s,v2) O (v4,t).(v3,t).(v5,t) O (s,v2),(v2,v3),(v2,v5) 0/3 -2/2- 4/5 -2/3 6/6 6/8