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.
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Graph
- The graph is a connected chain of five nodes...
b.
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Solutions
- There are n+1 solutions.
- Once any Xi is true, all subsequent Xjs must be true...
c.
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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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How 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.
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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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- How 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_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_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
- Consider 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_forwardPlease answer the following question in full detail. Please be specifix about everything: You have learned before that A∗ using graph search is optimal if h(n) is consistent. Does this optimality still hold if h(n) is admissible but inconsistent? Using the graph in Figure 1, let us now show that A∗ using graph search returns the non-optimal solution path (S,B,G) from start node S to goal node G with an admissible but inconsistent h(n). We assume that h(G) = 0. Give nonnegative integer values for h(A) and h(B) such that A∗ using graph search returns the non-optimal solution path (S,B,G) from S to G with an admissible but inconsistent h(n), and tie-breaking is not needed in A∗.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_forward
- Question # 22: Suppose you have a function f (x) = – cos (æhd two nodes -5 and 0. 1. Find the interpolation polynomial of the given function and nodes using the Vandermonde matrix method. 2. Roughly hand-draw a comparison graph between f ()and the interpolating polynomial. 3. Compute the actual interpolation error at a = 0arrow_forwardConsider a Local Search procedure such as Random Hill Climbing which employs the 2-change modification as neighbourhood function and the following instance of the Travelling Salesman Problem: 10 During the execution of the search, the highlighted (in bold) tour is visited. This current tour has a length of (62): [A → C → B → E → D → A] Select ALL correct statements. D a. The 2-change modification neighbourhood for TSP is reversible. O b. None of the statements is correct. O c. The modification, REMOVE ((A, C), (B, E)) and ADD ((A, B), (C, E)), is not a valid 2-change modification. O d. The current tour is a local minimum. O e. REMOVE ((A, D), (B, E)) and ADD ((A, B), (D, E)) is a valid 2-change modification, but not accepted for the next iteration step. O f. The modification, REMOVE ((A, D), (C, B)) and ADD ((C, D), (A, B)), yields in a tour which is accepted for the next iteration step. g. [A → C → B → E → D → A] is a neighbour of the tour [A → E → D → B → C → A] O h. The…arrow_forwardUsing this information: "MAX &SEPARATED MATCJ-JJNG INSTANCE: Graph G(V, E) and positive integer k. QUESTJON : Does G have a a-separated matching of size 2 k? Theorem 2.1. For each fixed 8 3 2, MAX &SEPARATED MATCHING is NP-complete. Moreover, this is true when restricted to bipartite graphs of degree 4. Proof. Fix some 6 a 2. Clearly the problem belongs to NP. We show that the NY-complete Vertex Cover Problem for graphs of degree 3 [2,3] is reducible to MAX S-SEPARATED MATCHING. VERTEXCOVER INSTANCE: QUESTION: Graph H(V, E) of degree 3, and integer k. Does H have a vertex cover of size or {bj, Cj} can be put in 9; this is a total of m edges. Say now that G has a a-separated matching M of size aam-l-n- k + 2m(6 - 2). There are two slightly different cases. Case 1. 6 = 2. (In this case there are no spikes.) We first transform M to a &separated matching M’ with IM’I 5 IMI such that (a) M’ contains no cross-edges, (b) for each j, 1 s j G m, M’ contains either {aj, cj] or {bj,…arrow_forward
- We mentioned that if we want to prove P ≠ NP, we only need to pick up any one NPC problem and prove that polynomial-time algorithm does not exist for the problem. If you want to prove P ≠ NP, select one NPC problem based on your preference and describe your idea of why polynomial-time algorithm does not exist for the problem. It does not have to be a formal proof, a description of your idea would be fine.arrow_forward1. Using the pumping lemma and contradiction, prove that L = (ab² n>=0} is not regular. 2. Using the pumping lemma and contradiction, prove that L = {a"bm n> m} is not regular. 3. Using the pumping lemma and contradiction, prove that L = (aºb narrow_forwardDraw the state space tree for the 5-Queen problem with a branching factor of 2. Show a local maxima in the state space tree if Hill Climbing is used to solve the problem. Note that you do not have to draw the whole state space tree. You can make up an initial state of your choice.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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