Artificial Intelligence: A Modern Approach
3rd Edition
ISBN: 9780136042594
Author: Stuart Russell, Peter Norvig
Publisher: Prentice Hall
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Chapter 4, Problem 8E
Explanation of Solution
a.
Proof:
- Since any state in a subset of “b” is in “b”, the result is immediate, an action sequence is a solution for belief state “b” if performing it starting in any state “s∈ b” reaches a goal state.
- Here it is proved that any action sequence which is not a solution for belief state b is also not a solution for any superset...
Explanation of Solution
b.
When adding the nodes, do not add to the frontier an...
Explanation of Solution
c.
If the user keeps a record of previously solved belief states, add a check to the beginning of OR-SEARCH t...
Expert Solution & Answer
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Check out a sample textbook solutionStudents have asked these similar questions
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.
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)
For each pair of graphs G1 = <V1, E1> and G2 = <V2, E2>
a) determine if they are isomorphic or not.
b) Determine a function that can be isomorphic between them if they are isomorphic. Otherwise you should justify why they are not isomorphic.
c) is there an Euler road or an Euler bike in anyone graph? Is Hamilton available? You should draw if the answer is yes and reason if your answer is no.
Chapter 4 Solutions
Artificial Intelligence: A Modern Approach
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(Note that we are considering directed graphs, so for a pair of vertices u and v there could be a path from u to v, but no path path from v back to u; in that case, u and v are not in the same strong component, even though they are connected by a path in one direction.) Given a vertex v in a directed graph D, design an algorithm for com- puting the strong connected…arrow_forward4. Let G = (V, E) be a graph with |V| = n. (a) Say what it means for G to be bipartite. (b) Is it true that every graph has a spanning subgraph that is bipartite? If yes, prove it, if no, find a counter-example. (c) Give the definition of a matching for G. Assuming G is bipartite with parts X and Y, state Hall's condition on the existence of a matching that saturates X.arrow_forwardLet G be the simple graph on the set V (G) = {p €N: p is prime, p = 1 mod 4, and p < 100} where uv e E(G) if and only if u # v and u = r has a solution modulo v. Draw this graph and answer the following questions. 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