Artificial Intelligence: A Modern Approach 2nd Edition Stuart Russell, Peter Norvig - Solutions

Discover a wealth of knowledge with our comprehensive solutions to "Artificial Intelligence: A Modern Approach, 2nd Edition" by Stuart Russell and Peter Norvig. Access the answers key and solutions manual, providing detailed solutions and step-by-step answers to the textbook's challenging problems. Our online platform offers a free download of the solutions PDF, including a test bank and instructor manual for enhanced learning. Whether you're tackling chapter solutions or seeking solved problems, our resource is designed to support your academic journey with expertly crafted questions and answers.

7.10 Write sentences to define the effects of the Shoot action in the wumpus world. As well as describing its effects on the wumpus, remember that shooting uses the agent's arrow.
7.8 Using the set axioms as examples, write axioms for the list domain, including all the constants, functions, and predicates mentioned in the chapter
7.7 Explain what is wrong with the following proposed definition of the set membership predicate G :\/x,s x£ {x\s}\/x,s xes => Vy x
7.6 Write axioms describing the predicates Grandchild GreatGrandparent, Brother, Sister, Daughter, Son, Aunt, Uncle, BrotherlnLaw, SisterlnLaw, and FirstCousin. Find out the proper definition of mth cousin n times removed, and write it in first-order logic.Write down the basic facts depicted in the
7.5 Represent the sentence "All Germans speak the same languages" in predicate calculus. Use Speaks(x, /), meaning that person x speaks language /.
7.4 Give a predicate calculus sentence such that every world in which it is true contains exactly one object.
6.16 Consider the problem of designing a logical agent for the wumpus world using a Boolean circuit—that is, a collection of logic gates connecting the inputs (percept values) to outputs(action values).a. Explain why you would need flip-flops.b. Give an order-of-magnitude estimate of how many
6.14 Implement a function VALIDITY that takes a sentence as input and returns either valid,—^ " satisfiable, or unsatisfiable. Use it to answer the questions in Exercise 6.12. You will need to define an implementation-level representation of sentences. The cleanest way to do this is to define an
6.13 What is the performance score that one could expect from the optimal wumpus world agent? Design an experiment wherein you look at all possible 4 x 4 wumpus worlds (or a random sample of them if there are too many), and for each one determine the shortest safe path to pick up the gold and
6.11 Provide a formal syntax, semantics, and proof theory for algebraic equations including variables, numbers, +, —, x, and -K You should be able to provide inference steps for most standard equation manipulation techniques.
6.10 We said it would take 64 prepositional logic sentences to express the simple rule "don't go forward if the wumpus is in front of you." What if we represented this fact with the single rule WumpmAhead => -^Forward Is this feasible? What effects does it have on the rest of the knowledge base?
6.9 Some agents make inferences as soon as they are told a new sentence, while others wait until they are asked before they do any inferencing. What difference does this make at the knowledge level, the logical level, and the implementation level?
6.8 We have defined four different binary logical connectives.a. Are there any others that might be useful?b. How many binary connectives can there possibly be?c. Why are some of them not very useful?
6.7 Consider a world in which there are only four propositions, A, B, C, and D. How many models are there for the following sentences?a. A f\Bb. A V B C. A A B A C
6.6 What ontological and epistemological commitments are made by the language of realnumber arithmetic?
6.5 (Adapted from (Barwise and Etchemendy, 1993).) Given the following, can you prove that the unicorn is mythical? How about magical? Horned?* ' If the unicorn is mythical, then it is immortal, but if it is not mythical, then it is a mortal mammal. If the unicorn is either immortal or a mammal,
6.4 Is the sentence "Either 2 + 2 = 4 and it is raining, or 2 + 2 = 4 and it is not raining" making a claim about arithmetic, weather, or neither? Explain.
6.1 We said that truth tables can be used to establish the validity of a complex sentence. Show how they can be used to decide if a given sentence is valid, satisfiable, or unsatisfiable.
5.17 We have assumed that the rules of each game define a utility function that is used by both players, and that a utility of x for MAX means a utility of — x for MIN. Games with this property are called zero-sum games. Describe how the minimax and alpha-beta algorithms change when we have
5.16 The minimax algorithm returns the best move for MAX under the assumption that MIN plays optimally. What happens when MIN plays suboptimally?
5.15 For a game with which you are familiar, describe how an agent could be denned with condition-action rules, subgoals (and their conditions for generation), and action-utility rules, instead of by minimax search.
5.14 Discuss how well the standard approach to game playing would apply to games such as tennis, pool, and croquet, which take place in a continuous, physical state space.
5.13 The Chinook checkers program makes extensive use of endgame databases, which provide exact values for every position within 6 moves of the end of the game. How might such databases be generated efficiently?
5.12 Consider carefully the interplay of chance events and partial information in each of the games in Exercise 5.11.a. For which is the standard expectiminimax model appropriate? Implement the algorithm and run it in your game-playing agent, with appropriate modifications to the game-playing
5.11 Describe and/or implement state descriptions, move generators, and evaluation functions for one or more of the following games: backgammon, Monopoly, Scrabble, bridge (declarer play is easiest).
5.10 Suppose we play a variant of Tic-Tac-Toe in which each player sees only his or her own moves. If the player makes a move on a square occupied by an opponent, the board "beeps" and the player gets another try. Would the backgammon model suffice for this game, or would we need something more
5.9 Describe and implement a general game-playing environment for an arbitrary number of players. Remember that time is part of the environment state, as well as the board position.
5.7 Consider the following procedure for choosing moves in games with chance nodes:• Generate a suitable number (say, 50) dice-roll sequences down to a suitable depth (say, 8).• With known dice rolls, the game tree becomes deterministic. For each dice-roll sequence, solve the resulting
5.6 Prove that with a positive linear transformation of leaf values, the move choice remains unchanged in a game tree with chance nodes.
5.4 The algorithms described in this chapter construct a search tree for each move from scratch.Discuss the advantages and disadvantages of retaining the search tree from one move to the next and extending the appropriate portion. How would tree retention interact with the use of selective search
5.3 Implement move generators and evaluation functions for one or more of the following games: kalah, Othello, checkers, chess. Exercise your game-playing agent using the implementation.Compare the effect of increasing search depth, improving move ordering, and improving the evaluation function.
5.2 Implement a general game-playing agent for two-player deterministic games, using alphabeta search. You can assume the game is accessible, so the input to the agent is a complete description of the state.
4.17 Compare the performance of A*, SMA*, and IDA* on a set of randomly generated problems in the 8-puzzle (with Manhattan distance) and TSP (with minimum spanning tree)domains. Discuss your results. What happens to the performance of IDA* when a small random number is added to the heuristic values
4.16 Prove that IDA* returns optimal solutions whenever there is sufficient memory for the longest path with cost < /*. Could it be modified along the lines of SMA* to succeed even with enough memory for only the shortest solution path?
4.12 Implement the n-queens problem and solve it using hill-climbing, hill-climbing with random restart, and simulated annealing. Measure the search cost and percentage of solved problems using randomly generated start states. Graph these against the difficulty of the problems(as measured by the
4.10 Would a bidirectional A* search be a good idea? Under what conditions would it be applicable? Describe how the algorithm would work.
4.9 We gave two simple heuristics for the 8-puzzle: Manhattan distance and misplaced tiles.Several heuristics in the literature purport to be better than either of these. (See, for example, Nilsson(1971) for additional improvements on Manhattan distance, and Mostow and Prieditis (1989)for
4.8 We showed in the chapter that an admissible heuristic heuristic (when combined with pathmax) leads to monotonically nondecreasing/ values along any path (i.e.,f(successor(n)) >/(«)). Does the implication go the other way? That is, does monotonicity in/ imply admissibility of the associated hi
4.7 Prove that if the heuristic function h obeys the triangle inequality, then the/-cost along any path in the search tree is nondecreasing. (The triangle inequality says that the sum of the costs from A to B and B to C must not be less than the cost from A to C directly.)
4.6 Invent a heuristic function for the 8-puzzle that sometimes overestimates, and show how it can lead to a suboptimal solution on a particular problem.
4.5 We saw on page 95 that the straight-line distance heuristic is misleading on the problem of going from lasi to Fagaras. However, the heuristic is perfect on the opposite problem: going from Fagaras to lasi. Are there problems for which the heuristic is misleading in both directions?
4.4 Sometimes there is no good evaluation function for a problem, but there is a good comparison method: a way to tell if one node is better than another, without assigning numerical values to either. Show that this is enough to do a best-first search. What properties of best-first search do we
4.3 Consider the problem of constructing crossword puzzles: fitting words into a grid of intersecting horizontal and vertical squares. Assume that a list of words (i.e., a dictionary) is provided, and that the task is to fill in the squares using any subset of this list. Go through a complete goal
4.2 Come up with heuristics for the following problems. Explain whether they are admissible, and whether the state spaces contain local maxima with your heuristic:a. The general case of the chain problem (i.e., with an arbitrary goal state) from Exercise 3.15.b. Algebraic equation solving (e.g.,
4.1 Suppose that we run a greedy search algorithm with h(ri) = —g(n). What sort of search will the greedy search emulate?
3.21 Implement a constraint satisfaction system as follows:a. Define a datatype for CSPs with finite, discrete domains. You will need to find a way to represent domains and constraints.b. Implement operators that assign values to variables, where the variables are assigned in a fixed order at each
3.20 Define each of the following as constraint satisfaction problems:a. The cryptarithmetic problem.b. The channel-routing problem in VLSI layout.c. The map-coloring problem. In map-coloring, the aim is to color countries on a map using a given set of colors, such that no two adjacent countries
3.19 In discussing the cryptarithmetic problem, we proposed that an operator should assign a value to whichever letter has the least remaining possible values. Is this rule guaranteed to produce the smallest possible search space? Why (not)?
3.18 The search agents we have discussed make use of a complete model of the world to construct a solution that they then execute. Modify the depth-first search algorithm with repeated state checking so that an agent can use it to explore an arbitrary vacuum world even without a model of the
3.15 The chain problem (Figure 3.20) consists of various lengths of chain that must be reconfigured into new arrangements. Operators can open one link and close one link. In the standard form of the problem, the initial state contains four chains, each with three links. The goal state consists of a
3.14 Consider the following operator for the 8-queens problem: place a queen in the column with the fewest unattacked squares, in such a way that it does not attack any other queens. How many nodes does this expand before it finds a solution? (You may wish to have a program calculate this for you.)
3.13 We said that at least one direction of a bidirectional search must be a breadth-first search.What would be a good choice for the other direction? Why?
3.12 Give the time complexity of bidirectional search when the test for connecting the two searches is done by comparing a newly generated state in the forward direction against all the states generated in the backward direction, one at a time.
3.11 Write down the algorithm for bidirectional search, in pseudo-code or in a programming language. Assume that each search will be a breadth-first search, and that the forward and backward searches take turns expanding a node at a time. Be careful to avoid checking each node in the forward search
3.10 Figure 3.17 shows a schematic view of bidirectional search. Why do you think we chose to show trees growing outward from the start and goal states, rather than two search trees growing horizontally toward each other?
3.9 Describe a search space in which iterative deepening search performs much worse than depth-first search.
3.8 Given a pathless search algorithm such as the one called for in Exercise 3.7, explain how you can modify the operators to keep track of the paths as part of the information in a state. Show the operators needed to solve the route-finding and touring problems.
3.7 The formulation of problem, solution, and search algorithm given in this chapter explicitly!mentions the path to a goal state. This is because the path is important in many problems. For 1 other problems, the path is irrelevant, and only the goal state matters. Consider the problem!"Find the
3.6 The GENERAL-SEARCH algorithm consists of three steps: goal test, generate, and ordering!function, in that order. It seems a shame to generate a node that is in fact a solution, but to fail to|recognize it because the ordering function fails to place it first.a. Write a version of GENERAL-SEARCH
3.5 On page 76, we said that we would not consider problems with negative path costs. In this exercise, we explore this in more depth.a. Suppose that a negative lower bound c is placed on the cost of any given step—that is, negative costs are allowed, but the cost of a step cannot be less thanc.
3.4 Implement the missionaries and cannibals problem and use breadth-first search to find the shortest solution. Is it a good idea to check for repeated states? Draw a diagram of the complete state space to help you decide.
3.3 Give the initial state, goal test, operators, and path cost function for each of the following.There are several possible formulations for each problem, with varying levels of detail. The main thing is that your formulations should be precise and "hang together" so that they could be
3.2 Consider the accessible, two-location vacuum world under Murphy's Law. Show that for each initial state, there is a sequence of actions that is guaranteed to reach a goal state.
3.1 Explain why problem formulation must follow goal formulation.
2.11 Experiment with changing the shape and dirt placement of the room, and with adding furniture. Measure your agents in these new environments. Discuss how their performance might be improved to handle more complex geographies.
2.10 Calculate the size of the table for a table-lookup agent in the domain of Exercise 2.7.Explain your calculation. You need not fill in the entries for the table.
2.9 Design and implement several agents with internal state. Measure their performance. How close do they come to the ideal agent for this environment?
2.8 Design and implement a pure reflex agent for the environment of Exercise 2.7, ignoring the requirement of returning home, and measure its performance. Explain why it is impossible to have a reflex agent that returns homeland shuts itself off. Speculate on what the best possible reflex agent
2.7 Implement an environment for anxm rectangular room, where each square has a 5% chance of containing dirt, and n and m are chosen at random from the range 8 to 15, inclusive.
2.6 Implement a table-lookup agent for the special case of the vacuum-cleaner world consisting of a 2 x 2 grid of open squares, in which at most two squares will contain dirt. The agent starts in the upper left corner, facing to the right. Recall that a table-lookup agent consists of a table of
2.5 Implement a performance-measuring environment simulator for the vacuum-cleaner world.This world can be described as follows:
2.4 While driving, which is the best policy?a. Always put your directional blinker on before turning,b. Never use your blinker,c. Look in your mirrors and use your blinker only if you observe a car that can observe you?What kind of reasoning did you need to do to arrive at this policy (logical,
2.3 Choose a domain that you are familiar with, and write a PAGE description of an agent for the environment. Characterize the environment as being accessible, deterministic, episodic, static, and continuous or not. What agent architecture is best for this domain?
2.2 For each of the environments in Figure 2.3, determine what type of agent architecture is most appropriate (table lookup, simple reflex, goal-based or utility-based).
2.1 What is the difference between a performance measure and a utility function?
1.10 "Surely animals cannot be intelligent—they can only do what their genes tell them." Is the latter statement true, and does it imply the former?
1.9 "Surely computers cannot be intelligent—they can only do what their programmers tell them." Is the latter statement true, and does it imply the former?
1.8 Some authors have claimed that perception and motor skills are the most important part of intelligence, and that "higher-level" capacities are necessarily parasitic—simple add-ons to these underlying facilities. Certainly, most of evolution and a large part of the brain have been devoted to
1.7 Fact, fiction, and forecast:a. Find a claim in print by a reputable philosopher or scientist to the effect that a certain capacity will never be exhibited by computers, where that capacity has now been exhibited.b. Find a claim by a reputable computer scientist to the effect that a certain
1.6 Find an article written by a lay person in a reputable newspaper or magazine claiming the achievement of some intelligent capacity by a machine, where the claim is either wildly exaggerated or false.
1.5 Examine the AI literature to discover whether or not the following tasks can currently be solved by computers:a. Playing a decent game of table tennis (ping-pong).b. Driving in the center of Cairo.c. Playing a decent game of bridge at a competitive level.d. Discovering and proving new
1.4 Suppose we extend Evans's ANALOGY program so that it can score 200 on a standard IQ test. Would we then have a program more intelligent than a human? Explain.
1.3 There are well-known classes of problems that are intractably difficult for computers, and other classes that are provably undecidable by any computer. Does this mean that AI is impossible?
1.2 We characterized the definitions of AI along two dimensions, human vs. ideal and thought vs. action. But there are other dimensions that are worth considering. One dimension is whether we are interested in theoretical results or in practical applications. Another is whether we intend our
1.1 Read Turing's original paper on AI (Turing, 1950). In the paper, he discusses several potential objections to his proposed enterprise and his test for intelligence. Which objections still carry some weight? Are his refutations valid? Can you think of new objections arising from developments
Implement a version of the chart-parsing algorithm that returns a packed tree of all edges that span the entire input.
Consider the sentence "Someone walked slowly to the supermarket" and the following lexicon:Pronoun -+ someone V -+ walked Adv -+ slowly Prep + to Det -+ the Noun -t supermarket Which of the following three grammars, combined with the lexicon, generates the given sentence?Show the corresponding
Without looking back at Exercise 22.1, answer the following questioAs:a. What are the four steps that are mentioned?b. What step is left out?c. What is "the material" that is mentioned in the text?d. What kind of mistake would be expensive?e. Is it better to do too few or too many? Why?
Determine what semantic interpretation would be given to the following sentences by the grammar in this chapter:a. It is a wumpus.b. The wumpus is dead.c. The wumpus is in 2,2.Would it be a good idea to have the semantic interpretation for "It is a wumpus" be simply 3 x x E Wumpuses? Consider
Augment the El grammar so that it handles article-noun agreement. That is, make sure that "agents" is an NP, but "agent" and "an agents7' are not.
Implement the REINFORCE and PEGASUSa lgorithms and apply them to the 4 x 3 world, using a policy family of your own choosing. Comment on the results.
Extend the standard game-playing environment (Chapter 6) to incorporate a reward signal. Put two reinforcement learning agents into th~e environment (they may, of course, share the agent program) and have them play against each other. Apply the generalized TD update rule (Equation (21.11)) to
Compute the true utility function and the best linear approximation in x and y (as in Equation (21.9)) for the following environments:a. A 10 x 10 world with a single $1 terminal state at (10,lO).b. As in (a), but add a -1 terminal state at (10,l).c. As in (b), but add obstacles in 10 randomly
Write out the parameter update equations for TI) learning with - (x,y) =00+01+02y+03 (xg)2 + (y-g)2
Implement an exploring reinforcement learning agent that uses direct utility estimation.Make two versions-ne with a tabular representation and one using the function approximator in Equation (21.9). Compare their performance in three environments:a. The 4 x 3 world described in the chapter.b. A 10
Adapt the vacuum world (Chapter 2) for reinforcement learning by including rewards for picking up each piece of dirt and for getting home and switching off. Make the world accessible by providing suitable percepts. Now experiment with different reinforcement learning agents. Is function
Chapter 17 defined a proper policy for an MDP as one that is guaranteed to reach a terminal state. Show that it is possible for a passive ADP agent to learn a transition model for which its policy n is improper even if n is proper for the true MDP; with such models, the value determination step may
Consider the problem of separating N data points into positive and negative examples using a linear separator. Clearly, this can always be done for N = 2 points on a line of dimension d = 1, regardless of how the points are labelled or where they are located (unless the points are in the same
Suppose that a training set contains only a single example, repeated 100 times. In 80 of the 100 cases, the single output value is 1; in the other 20, it is 0. What will a backpropagation network predict for this example, assuming that it has been trained and reaches a global optimum? (Hint: to
Starting from Equation (20.13), show that dL/aWj = Err x xj.

Showing 4400 - 4500 of 4756

First
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48

Artificial Intelligence: A Modern Approach 2nd Edition Stuart Russell, Peter Norvig - Solutions

Step by Step Answers