Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Chapter 7, Problem 15E
a.
Explanation of Solution
Graph
- The graph is a connected chain of five nodes...
b.
Explanation of Solution
Solutions
- There are n+1 solutions.
- Once any Xi is true, all subsequent Xjs must be true...
c.
Explanation of Solution
Complexity
- The complexity is O(n2).
- The
algorithm must follow all solution sequences, which thems...
d.
Explanation of Solution
Horn problem
- These facts are not obviously connected.
- Horn-form logical inference problems need not ha...
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True/False. Give a short explanation.
i. Let T be a tree constructed by Dijkstra's algorithm for a weighted connected graph
G. T is a spanning tree of G?
ii. Let T be a tree constructed by Dijkstra's algorithm for a weighted connected graph
G. T is a minimum spanning tree of G?
iii. If an NP-complete problem can be solved in linear time, then all NP-complete
problems can be solved in linear time.
iv. If P # NP, there could be a polynomial-time algorithm for SAT.
True or False (If your answer to the question is "False", explain why, and provide correction when possible). (a) Let h(n) be the heuristics for the node n, h(m) be the heuristics for the node m, d(m,n) be the actual minimal cost from node m to n in a graph. A* satisfies the monotone restriction iff d(m,n) <= |h(n)-h(m)|.
(b) If an A* heuristics is admissible then it satisfies the monotone restriction.
(c) Best-first search guarantees optimality in its returned solution.
(d) Least-cost-first search guarantees optimality in its returned solution.
(e) If all edges are with unit cost, then Breadth-first search guarantees optimality in its returned solution.
Show that the 3-CNF satisfiability problem (3-CNF SAT ) is NP-complete.
Chapter 7 Solutions
Artificial Intelligence: A Modern Approach
Ch. 7 - Suppose the agent has progressed to the point...Ch. 7 - (Adapted from Barwise and Etchemendy (1993).)...Ch. 7 - Prob. 3ECh. 7 - Which of the following are correct? a. False |=...Ch. 7 - Prob. 5ECh. 7 - Prob. 6ECh. 7 - Prob. 7ECh. 7 - We have defined four binary logical connectives....Ch. 7 - Prob. 9ECh. 7 - Prob. 10E
Ch. 7 - Prob. 11ECh. 7 - Prob. 12ECh. 7 - Prob. 13ECh. 7 - Prob. 14ECh. 7 - Prob. 15ECh. 7 - Prob. 16ECh. 7 - Prob. 17ECh. 7 - Prob. 18ECh. 7 - A sentence is in disjunctive normal form (DNF) if...Ch. 7 - Prob. 20ECh. 7 - Prob. 21ECh. 7 - Prob. 23ECh. 7 - Prob. 24ECh. 7 - Prob. 25ECh. 7 - Prob. 26ECh. 7 - Prob. 27E
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Similar questions
- The following is an instance of the conjunctive normal form (CNF) problem. (x1 V 2 V x3) ^ (x3 V¤1) ^ (x2 V x3) Transform this problem into a clique problem. The solution to this CNF problem is not unique. Use the graph to find 3-member cliques. Each column should contain 1 member. Find as many cliques as you can find. Find their corresponding CNF solutions.arrow_forwardIn the Euclidean (metric) Traveling Salesperson Problem (TSP), we started with a DFS traversal of the minimum spanning tree (MST) and then skipped vertices that we had already visited. Why were we able to allow skipping of nodes? O Because DFS run on an MST adds an exponential number of vertices O In a metric space the triangle inequality states that removing a vertex cannot lengthen the path O In the Euclidean metric, distance in measured in the number of edges, so removing edges makes the path shorter O It feels rightarrow_forwardConsider a problem with four variables, {A,B,C,D}. Each variable has domain {1,2,3}. The constraints on the problem are that A > B, B < C, A = D, C ¹ D. Perform variable elimination to remove variable B. Explain the process and show your work.arrow_forward
- Let A = {x ∈ Z : x ≤ 3} and let B = {x ∈ Q : x2 = 9}. Is B ⊆ A? Give a brief reason for your answer.arrow_forwardHow would you modify the dynamic programming algorithm for the coin collecting problem if some cells on the board are inaccessible for the robot? Apply your algorithm to the board below, where the inaccessible cells are shown by X’s. How many optimal paths are there for this board? You need to provide 1) a modified recurrence relation, 2) a pseudo code description of the algorithm, and 3) a table that stores solutions to the subproblems.arrow_forwardGiven a system of difference constraints. Let G=(V,E) be the corresponding constraint graph. By applying BELLMAN_FORD's algorithm on v0 (v0 is the source vertex), the number of vertices who's shortest paths will be updated is at the second iteration. x1 - x2 ≤ 7 x1 - x3 ≤ 6 x2 - x4 ≤ -3 x3 - x4 ≤ -2 x4 - x1 ≤ -3arrow_forward
- True or False (If your answer to the question is "False", explain why, and provide correction when possible). (a) Let h(n) be the heuristics for the node n, h(m) be the heuristics for the node m, d(m,n) be the actual minimal cost from node m to n in a graph. A* satisfies the monotone restriction iff d(m,n)arrow_forwardIt was claimed that:(a, b) ≤ (c, d) ⇔ (a < c) ∨ (a = c ∧ b ≤ d) defines a well-ordering on N x N. Show that this is actually the case.arrow_forwardConsider the following generalization of the maximum matching problem, which we callStrict-Matching. Recall that a matching in an undirected graph G = (V, E) is a setof edges such that no distinct pair of edges {a, b} and {c, d} have endpoints that areequal: {a, b} ∩ {c, d} = ∅. Say that a strict matching is matching with the propertythat no pair of distinct edges have endpoints that are connected by an edge: {a, c} ̸∈ E,{a, d} ̸∈ E, {b, c} ̸∈ E, and {b, d} ̸∈ E. (Since a strict matching is also a matching, wealso require {a, b} ∩ {c, d} = ∅.) The problem Strict-Matching is then given a graphG and an integer k, does G contain a strict matching with at least k edges.Prove that Strict-Matching is NP-complete.arrow_forward
- The third-clique problem is about deciding whether a given graph G = (V, E) has a clique of cardinality at least |V |/3.Show that this problem is NP-complete.arrow_forward3. Given the following example of UAG graphs: 12 12 6. 10 21 5 3 5 3 5 \21 14 15 8 15 8. Graph A Graph B Graph C (degree(v) <= 1) a) Give implementation to find the shortest path b) Does your implementation take all considerations and could accept any kind of inputs? Explain c) Justify your choice by providing the approximating time/space complexity of each type graph. 3.arrow_forwardhow could someone solce this one? The Chinese postman problem: Consider an undirected connected graph and a given starting node. The Chinese postman has to find the shortest route through the graph that starts and ends in the starting node such that all links are passed. The same problem appears for instance for snow cleaning or garbage collection in a city. For a branch-and-bound algorithm, find a possible lower bound function. (Remark: If the problem is to pass through all nodes of the graph, it is called the travelling salesman problem - which needs different solution algorithms, but also of the branch-and-bound type).).arrow_forward
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