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- The Harvard robotics club has organized a Robothon. n robots are placed alongthe edge of a circular area at the middle of the OAT(open air theatre). Each robot will move along arbitrary tracksinside the circle while leaving behind a heat signature along its trail. However, they have beenprogrammed not to cross their own trail or the trail of another robot, neither will they ever moveout of the circle. In case a pair of robots i and j meet at any point, they are removed from the sceneand the club will pay a reward sum of M[i, j] to the owners of these robots. Note that some robotscan keep moving infinitely without ever meeting another one. Given the reward matrix M whereM[i, j] = M[j, i], design a polynomial time algorithm that determines the maximum money theclub might potentially end up spending. For this particular problem, give a very brief justificationof the recurrence. Give pseudo-code for a dynamic program which solves the recurrence efficiently Youdo not need to prove…. The vacuum cleaner problem is a well-known search problem for a vacuum cleaner robot that works on Artificial Intelligence. In this problem to clean up the whole area. In the superficial world, the vacuum cleaner agent has a location sensor and a dirt sensor to know where it is (room A, room B, or any n room) and whether the room is dirty. Also, the robot needs to avoid the obstacle (stool) and find a new path. A possible performance measure is to maximize the number of clean rooms over a certain period. For this problem, four main conditions should be considered: in(x,y) means a robot at (x,y) dirt(x,y) means there is a dirt at(x,y) facing(d) means the robot is facing direction d, where d ={north, east, south, west} • hit(s) means the robot hits the obstacle s possible actions the robot can do - turn, forward, suck-dirt, avoid a) Write possible rules that can be used to perform the room cleaning plan b) Execute this plan…You are developing a simulation model of a service system and are trying to create an input model of the customer arrival Process, You have the following four observations of the process of interest [86, 24,9, 50] and you are considering either an exponential distribution Of a uniform distribution for the model. Using the data to estimate any necessary distribution Parameters, write the steps to plot Q-Q plots for both cases i.e. exponential and uniform.
- . Draw the ERD for the following scenario. In a university, a Lecturer can teach many different courses and even the same course numerous times. Courses can also be taught by many lecturers. A student is enrolled in only one program but a program can contain many students. Students can be rolled in many courses at the same time and the courses have many students enrolled.Implement an algorithmic solution, indicating which states are valid and which are not, and model the space of the following problem: An interest group from a small town decided to sue a company for commercial abuse. For this, the people have organized themselves and decided to send 3 representatives, who will have to travel in a Van to the city where the lawsuit will be filed. The company to be sued, upon learning of these actions, has decided to send 3 lawyers to persuade the representatives, who will also travel in the same Van for that purpose. The community must file the class action suit under these conditions: - The three applicants must reach the destination city; - Only two people can travel per trip in the Van (small town - city, city - small town); - There can never be more lawyers than plaintiffs in any one place (either in the small town or city) because the lawyers can persuade the plaintiffs and as a consequence, the lawsuit would not be made; - The Van cannot be…In a prison, there is a door b/w any pair of adjacent cells and one exit guarded by a guard G. One prisoner is a maniac M which kills anybody he can see when he enters a cell. If M returns to the cell with his victim, then he loses consciousness and stops. In the evening all inmates and the guard went to sleep in their cells. In the morning, maniac M is gone and all other prisoners with the guard were found dead in their cells. Show the route of the maniac.
- Assume we have a game that uses synchronized simulation. If we want to extendthe game by including new players, which will become the limiting factor first: thenumber of human players or the number of synthetic players?We can implement requests to the waiter as either a queue of requests or as a periodic retry of a request. With a queue, requests are handled in the order they are received. Th e problem with using the queue is that we may not always be able to service the philosopher whose request is at the head of the queue (due to the unavailability of resources). Describe a scenario with 5 philosophers where a queue is provided, but service is not granted even though there are forks available for another philosopher (whose request is deeper in the queue) to eat.If we implement requests to the waiter by periodically repeating our request until the resources become available, will this solve the problem described in the above Exercise? Explain.(i) Describe Banker’s algorithm for deadlock avoidance with supporting example Consider a computer system with has four identical units of a resource R. There are three processes each with a maximum claim of two units of resource R. Processes can request these resources in anyway, that is, two in one shot or one by one. The system always satisfies a request a request for a resource if enough resources are available. If the process doesn’t request any other kind of resource, show that the system never deadlock Give a solution for the following synchronization problem using semaphores Producer- Consumer Problem Readers- Writers Problem List out the issues in preprocessor scheduling that causes performance degradation in multiprocessor systems
- You are developing a simulation model of a service system and are trying to create aninput model of the customer arrival Process, You have the following four observations of the process of interest [86, 24,9, 50] and you are considering either an exponential distributionOf a uniform distribution for the model. Using the data to estimate any necessary distributionParameters, write the steps to plot Q-Q plots for both cases.A wave is modeled by the wave function: y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)] y1 (t) = A sin (2πf1t) y2 (t) = A sin (2πf2t) Using any computer program, construct the wave dependency graph resultant y (t) from time t in the case when the frequencies of the two sound waves are many next to each other if the values are given: A = 1 m, f1 = 1000 Hz and f2 = 1050 Hz. Comment on the results from the graph and determine the value of the time when the waves are with the same phase and assemble constructively and the time when they are with phase of opposite and interfere destructively. Doing the corresponding numerical simulations show what happens with the increase of the difference between the frequencies of the two waves and vice versa.Consider a robot that is capable of picking objects from a shelf and placing them on the table. Suppose that the robot’s arm works perfectly, and the environment is fully-observable. (i) Define a STRIPS operator that could be used for planning the actions of this robot. (ii) Give an example of a state S of the world at which this STRIPS operator is applicable. (iii) Describe the operation of this STRIPS operator at this state S, to show the next state S0 of the world.