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- link(a,b). link(a,c). link(b,c). link(b,d). link(c,d). link(d,e). link(d,f). link(e,f). link(f,g). Using The above Formulate the appropriate Prolog predicate "path(X,Y,N)" which is true if (and only if) there is a path of length "N" from node "X" to node "Y". For example, there is a path of length 2 from "a" to "d": "a->b->d", but also "a->c->d", and so "path(a,d,2)" gives "true" (two times). There is also a path of length 3 from "a" to "d": "a->b->c->d". Test this predicate out on the above network to verify whether or not it is working correctly. Once this is working correctly, note now, that e.g., "path(a,e,N)." will give multiple answers: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.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.
- Please answer the following question in depth with full detail. Consider the 8-puzzle that we discussed in class. Suppose we define a new heuristic function h3 which is the average of h1 and h2, and another heuristic function h4 which is the sum of h1 and h2. That is, for every state s ∈ S: h3(s) =h1(s) + h2(s) 2 h4(s) =h1(s) + h2(s) where h1 and h2 are defined as “the number of misplaced tiles”, and “the sum of the distances of the tiles from their goal positions”, respectively. Are h3 and h4 admissible? If admissible, compare their dominance with respect to h1 and h2, if not, provide a counterexample, i.e. a puzzle configuration where dominance does not hold.Suppose we want to use UCS and the A* algorithm on the graph below to find the shortest path from node S to node G. Each node is labeled by a capital letter and the value of a heuristic function. Each edge is labeled by the cost to traverse that edge. Perform A*, UCS, and BFS on this graph. Indicate the f, g, and h values of each node for the A*. e.g., S = 0 + 6 = 6 (i.e. S = g(S) + h(S) = f(S)). Additionally, show how the priority queue changes with time. Show the order in which the nodes are visited for BFS and UCS. Show the path found by the A*, UCS, and BFS algorithms on the graph above. Make this example inadmissible by changing the heuristic value at one of the nodes. What node do you choose and what heuristic value do you assign? What would be the A* algorithm solution then.Consider a fully-connected artificial neural network with one hidden layer, i.e., a multilayer perceptron (MLP), which has 5 inputs, 3 neurons in the hidden layer, and 1 output neuron. The relation between the output y and the inputs x = [x1, . . . , x5] is given by y(x) = f (w, φ(x)), where φ(x) = [φ1(x), φ2(x), φ3(x)] 1. Draw the diagram that shows the inputs, nuerons, connections, correspond-ing weight parameters, and activation functions. 2. Explain the relation y(x) = f (w, φ(x)): write the explicit relation, explainthe role of functions f and φ(x), and state examples of functions.
- For each pair of atomic sentences, give the most general unifier if it exists: 1. P(N, M, z), P(x, y, N). 2. Q(x, y, M), Q(N, M, x). 3. Knows(y, y), Knows(Father(x), x).Given an abstraction of the City Tube Map where each node represents the city’s attraction, plan the trip for the tourist to visit. Start from node 1 that is their hotel, a group of tourists wants to visit all places. However, due to the time limitation, they can only visit each attraction once. To find the best order of places to visit, genetic algorithm can be used to derive the best possible solutions.Review the 8-puzzle problem. Consider that the initial state is 1 3 48 27 6 5and the goal state is1 2 38 47 6 5Apply the breath-first-search method to obtain the path from the initial state to the goal state. Youneed to show the corresponding search tree. As soon as you find the goal state, you can stop the searchprocess.
- Simulate the node expansion from start state (S) to reach goal state (G) using BFS, DFS, UCS, Greedy, A*, and also given heuristic function that h(A) = 8 , h(B) = 9, h(C) = 7, h(D) = 5, h(F) = 4, h(H) = 2, h(G) = 0, h(J) = 3,h(I) = 1Implement a graphical system to manage employees using an employee id, employee name, and years of service. The system should usea B-tree of order 7 to store employees, and it must provide the abilityto add and remove employees. After each operation, your system mustupdate a sorted list of employees sorted by name on the screen.link(a,b). link(a,c). link(b,c). link(b,d). link(c,d). link(d,e). link(d,f). link(e,f). link(f,g). Using the above Formulate the appropriate Prolog predicate "path(X,Y,N)" which is true if (and only if) there is a path of length "N" from node "X" to node "Y". For example, there is a path of length