Artificial Intelligence A Modern Approach 2nd Edition Stuart J. Russell and Peter Norvig - Solutions

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Define in your own words:(a) Intelligence,(b) Artificial intelligence,(c) Agent.
Read Turing’s original paper on Al (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? Arc his refutations valid? Can you think of new objections arising from developments since
Every year the Loebner prize is awarded to the program that comes closest to passing a version of the Turing test. Research and report on the latest winner of the Loehner prize. What techniques does it use? How does it advance the state of the art in AI?
There are well-known classes of problems that are intractably difficult for computers, and other classes that are provably un-decidable. Does this mean that Al is impossible?
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.
How could introspection—reporting on one’s inner thoughts—be inaccurate? Could I be wrong about what I’m thinking? Discuss.
Examine the Al literature to discover whether 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. Buying a week’s worth of groceries at the market.d. Buying a week’s worth of groceries on the webe.
Sonic 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
Why would evolution tend to result in systems that act rationally? What goals are such systems designed to achieve?
Are reflex actions (such as moving your hand away from a hot stove) rational? Are they intelligent?
“Surely computers cannot be intelligent—they can do only what their programmers tell them.” Is the latter statement true, and does it imply the former?
“Surely animals cannot he intelligent—they call do only what their programmers tell them.” Is the latter statement true, and does it imply the former?
“Surely animals, humans, and computers cannot be intelligent—they can do only what their constituent atoms are told to do by the laws of physics.” Is the latter statement true, and does it imply the former?
Define in your own words the following terms: agent, agent function, agent program, rationality, autonomy, reflex agent, model-based agent, goal-based agent, utility-based agent, learning agent.
Both the performance measure and the utility function measure how well an agent is doing. Explain the difference between the two.
This exercise explores the differences between agent functions and agent programs.a. Can there be more than one agent program that implements a given agent function? Give an example, or show why one is not possible.b. Are there agent functions that cannot be implemented by any agent program?c.
Let us examine the rationality of various vacuum-cleaner agent functions.a. Show that the simple vacuum-cleaner agent function described in Figure is indeed rational tinder the assumptions listed.b. Describe a rational agent function for the modified performance measure that deducts one point for
For each of the following agents, develop a PEAS description of the task environment:a. Robot soccer player,b. Internet book-shopping agent;c. Autonomous Mars rover;d. Mathematician’s theorem-proving assistant.
For each of the agent types listed in Exercise 2.5, characterize the environment according to the properties given in Section 2.3, and select a suitable agent design. The following exercises all concern the implementation of environments and agents for the vacuum-cleaner world.
Implement a simple reflex agent for the vacuum environment in Exercise 2.7. Run the environment simulator with this agent for all possible initial dirt configurations and agent locations. Record the agent’s performance score for each configuration and its overall average score.
Consider a modified version of the vacuum environment in Exercise 2.7, in which the geography of the environment—its extent, boundaries, and obstacles—is unknown, as is the initial dirt configuration. (The agent can go Up and Doum as well as Left and Right.)a Can a simple reflex agent be
Repeat Exercise 2.10 for the case in which the location sensor is replaced with a “bump” sensor that detects the agent’s attempts to move into an obstacle or to cross the boundaries of the environment. Suppose the bump sensor stops working; how should the agent behave?
The vacuum environments in the preceding exercises have all been deterministic. Discuss possible agent programs for each of the following stochastic versions:a. Murphy’s Law twenty-five percent of the time, the Suck action fails to clean the floor if it is dirty and deposits dirt onto the floor
Define in your own words the following terms: state, state space, search tree, search node, goal, action, successor function, and branching factor.
Explain why problem formulation must follow goal formulation.
Suppose that legal-actions(s) denotes the set of actions that are legal in state s, and result(a, s) denotes the state that results from performing a legal action a in state s. define successor-en in terms of legal-actions and result, and vice versa.
Show that the 8-puizle states are divided into two disjoint sets, such that no state in one set can be transformed into a state in the other set by any number of moves. Devise a procedure that will tell you which class a given state is in, and explain why this is a good thing to have for generating
Consider the n-queens problem using the “efficient” incremental formulation given. Explain why the state space size is at least and estimate the largest ii for which exhaustive exploration is feasible.
Does a finite state space always lead to a finite search tree? How about a finite state space that is a tree? Can you be more precise about what types of state spaces always lead to finite search trees? (Adapted from Bender, 1996)
Give the initial state, goal test, successor function, and cost function for each of the following. Choose a formulation that is precise enough to be implemented.a. You have to color a planar map using only four colors, in such a way that no two adjacent regions have the same color.b. A 3-foot-tall
Consider a state space where the start state is number 1 and the successor function for state n returns two states, numbers 2n and 2n + 1.a. Draw the portion of the state space for states 1 to 15.b. Suppose the goal state is 11. List the order in which nodes will be visited for breadth- first
We mentioned iterative lengthening search, an iterative analog of uniform cost search. The idea is in use increasing limits on path cost. If a node is generated whose path cost exceeds the current limit, it is immediately discarded, for each new iteration the limit is set to the lowest path cost of
Prove that uniform-cost search and breadth-first search with constant step costs are optimal when used with the GRAPH-SEARCH algorithm. Show a state space with constant step costs in which GRAPH-SEARCH using iterative deepening finds a suboptimal solution.
Describe a state space iii which iterative deepening search performs much worse than depth-first search (for example. O(n2) vs. O(n)).
Write a program that will take as input two Web page URLs and find a path of links from one to the other. What is an appropriate search strategy is bidirectional search a good idea? Could a search engine be used to implement a predecessor function?
We said that we would not consider problems with negative path costs. In this exercise, we explore this in more depth.a. Suppose that actions can have arbitrarily large negative costs; explain why this possibility would force any optimal algorithm to explore the entire state space.b. Does it help
Consider the sensor less, two-location vacuum world under Murphy’s Law. Draw the belief state space reachable from the initial belief state {1, 2, 3, 4, 5, 6, 7, 8), and explain why the problem is unsolvable. Show also that if the world is fully observable then there is a solution sequence for
Trace the operation of A* search applied to the problem of getting to Bucharest from Lugoj using the straight line distance heuristic. That is, show the sequence of nodes that the algorithm will consider and the f, y, and h score for each node.
The heuristic path algorithm is a best-first search in which the objective function is f(n) = (2 – w) g(n) + wh(n). For what values of w is this algorithm guaranteed o be optimal? (You may assume that h is admissible.) What kind of search does this perform when w = 0? When w = 1? When w = 2?
Prove each of the following statements:a. Breadth-first search is a special case of uniform-cost search.b. Breadth-first search, depth-first search, and uniform-cost search are special cases of best-first search.c. Uniform-cost search is a special case of A* search.
Devise a state space in which A* using GRAPH-SEARCH returns a suboptimal solution with an h(n) function that is admissible but inconsistent.
We saw that the straight-line distance heuristic leads greedy best-first search astray 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?
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. (You can use a computer to help if you want.) Prove that, if h never overestimates by more than c, a using h returns a solution whose cost exceeds
Prove that if a heuristic is consistent, it must be admissible. Construct an admissible heuristic that is not consistent.
The traveling salesperson problem (TSP) can be solved via the minimum spanning tree (MST) heuristic, which is used to estimate the cost of completing a tour, given that a partial tour has already been constructed. The MST cost of a set of cities is the smallest sum of the link costs of any tree
We defined the relaxation of the 8-puzzle in which a tile can move from square A to square B if B is blank. The exact solution of this problem defines Gaschnig’s heuristic (Gaschnig, 1979). Explain why Gaschnig’s heuristic is at least as accurate as (misplaced tiles), and show cases where it is
Give the name of the algorithm those results from each of the following special cases:a. Local beam search with k = 1.b. Local beam search with one initial state and no limit on the number of states retained.c. Simulated annealing with T = 0 at all times (and omitting the termination test).d.
Sometimes there is no good evaluation function for a problem, but there is a good comparison method: a way to tell whether one node is better than another, without assigning numerical values to either. Show that this is enough to do a best-first search. Is there an analog of A*?
Relate the time complexity of LRTA* to its space complexity.
Suppose that an agent is in a 3 x 3 maze environment like the one shown in Figure. The agent knows that its initial location is (1, 1), that the goal is at (3, 3), and that the four actions Up, Down, Left, Right have their usual effects unless blocked by a wall. The agent does not know where the
In this exercise, we will explore the use of local search methods to solve TSPs of the type defined in Exercise 4.8.a. Devise a hill-climbing approach to solve TSPs. Compare the results with optimal solutions obtained via the A* algorithm with the MST heuristic (Exercise 4.8).
In this exercise, we will examine hill climbing in the context of robot navigation, using the environment in Figure as an example. a. Repeat Exercise 3.16 using hill climbing. Does your agent ever get stuck in a local minimum? Is it possible for it to get stuck with convex obstacles? b. Construct a
Compare the performance of A and RBFS on a set of randomly generated problems in the 8-puzzle (with Manhattan distance) and TSP (with MST—see Exercise 4.8) domains. Discuss your results. What happens to the performance of RBFS when a small random number is added to the heuristic values in the
Define in your own words the terms constraint satisfaction problem, constraint, backtracking search, arc consistency, back jumping and mm-conflicts.
How many solutions are there for the map-coloring problem inFigure?
Explain why it is a good heuristic to choose the variable that is most constrained, but the value that is 1act constraining in a CSP search
Consider the problem of constructing (not solving) crossword puzzles:5 fitting words into a rectangular grid. The grid, which is given as part of the problem, specifics which square are blank and which are shaded. Assume that a list of words (i.e., a dictionary) is provided and that the task is to
Give precise formulations for each of the following as constraint satisfaction problems:a. Rectilinear floor-planning: find non-overlapping places in a large rectangle for a number of smaller rectangles.b. Class scheduling: There is a fixed number of professors and classrooms, a list of classes to
Solve the crypt arithmetic problem in Figure by hand, using backtracking, forward checking, and the MRV and least-constraining-valueheuristics.
Use the AC-3 algorithm to show that arc consistency is able to detect the inconsistency of the partial assignment {WA = red, V = blue} for the problem shown inFigure.
What is the worst-case complexity of running AC-3 on a tree-structured CSP?
AC-3 puts back on the queue every arc (Xk, Xi) whenever any value is deleted from the domain of Xi, even if each value of Xk is consistent with several remaining values of X. Suppose that, for every arc (Xk, Xi), we keep track of the number of remaining values of Xk that are consistent with each
Show how a single ternary constraint such as “A + B = C” can be turned into three binary constraints by using an auxiliary variable. You may assume finite domains. Next, show how constraints with more than three variables can be treated similarly. Finally, show how unary constraints can be
Suppose that a graph is known to have a cycle cut set of no more than k nodes. Describe a simple algorithm for finding a minimal cycle cut set whose runtime is not much more than Q(nk) for a CSP with n variables. Search the literature for methods for finding approximately minimal cycle cut sets in
Consider the following logic puzzle: In five houses, each with a different color, live 5 persons of different nationalities, each of whom prefer a different brand of cigarette, a different drink, and a different pet. Given the following facts, the question to answer is “Where does the zebra live,
This problem exercises the basic concepts of game playing, using tic-tac-toe (noughts and crosses) as an example. We define Xn as the number of rows, columns, or diagonals with exactly n X’s and no O’s Similarly, On is the number of rows, columns, or diagonals with just n O’s. The utility
Prove the following assertion: for every game tree, the utility obtained by MAX using mini max decisions against a suboptimal MIN will be never be lower than the utility obtained playing against an optimal MIN. Can you come up with a game tree in which MAX can do still better using a suboptimal
Consider the two-player game described in Figure.a. Draw the complete game tree, using the following conventions:• Write each state as (SA, SB) where SA and 5B denote the token locations.• Put each terminal state in square boxes and write its game value in a circle.• Put loop states (states
Develop a formal proof of correctness for alpha-beta pruning. To do this, consider the situation shown in Figure. The question is whether to prune node nj, which is a max- node and a descendant of node n1. The basic idea is to prune it if and only if the mini max value of n can be shown to be
Prove that with a positive linear transformation of leaf values (i.e., transforming a value x to ax + b where a > 0), the choice of move remains unchanged in a game tree, even when there are chance nodes.
Consider the following procedure for choosing moves in games with chance nodes;• Generate some die-roll sequences (say, 50) down to a suitable depth (say, 8).• With known die rolls, the game tree becomes deterministic. For each die-roll sequence, solve the resulting deterministic game tree
Describe or implement state descriptions, move generators, terminal tests, utility functions, and evaluation functions for one or more of the following games: Monopoly, Scrabble, bridge (assuming a given contract), and poker (choose your favorite variety).
Consider carefully the interplay of chance events and partial information in each of the games in Exercise 6.10.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
The mini max algorithm assumes that players take turns moving, but in card games such as whist and bridge, the winner of the previous trick plays first on the next trick.a. Modify the algorithm to work properly for these games. You may assume that a function WINNER(s) is available that reports
The Chinook checkers program makes extensive use of endgame databases, which provide exact values for every position with eight or fewer pieces. How might such databases be generated efficiently?
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.
Describe how the mini max and alpha—beta algorithms change for two-player, nonzero-sum games in which each player has his or her own utility function. You may assume that each player knows the other’s utility function. if there are no constraints on the two terminal utilities, is it possible
Suppose you have a chess program that can evaluate 1 million nodes per second. Decide on a compact representation of a game state for storage in a transposition table. About how many entries can you fit in a 500MB in-memory table’? Will that be enough for the three minutes of search allocated for
Describe the wumpus world according to the properties of task environments listed.
Suppose the agent has progressed to the point shown in Figure (a) having perceived nothing in [1, 1], a breeze in [2, 1], and a stench in [1, 2], and is now concerned with the contents of [1, 3], [2, 2], and [3, 1]. Each of these can contain a pit and at most one can contain a wumpus. Following the
Consider the problem of deciding whether a propositional logic sentence is true in a given model.a. Write a recursive algorithm PL-TRUE? (s m) that returns true if and only if the sentence s is true in the model in (where in assigns a truth value for every symbol in s). The algorithm should run in
Prove each of the following assertions:a. α is valid if and only if True | = α.b. For any a, False | = α.c. α | = β if and only if the sentence (α → β) is valid.d. α ≡ β if and only if the sentence (α ↔ β) is valid.e. α | = β if and only if the sentence (α ^ β) is un-satisfiable
Consider a vocabulary with only four propositions, A, B, C, and D. How many models are there for the following sentences?a. (A Λ AB) V (B Λ C)b. A V Bc. A ↔ B ↔ C
We have defined four different binary logical connectives.a. Are there any others that might be useful?b. How many binary connectives can there be?c. Why are some of them not very useful?
Using a method of your choice, verify each of the equivalences inFigure.
Decide whether each of the following sentences is valid, un-satisfiable, or neither. Verify your decisions using truth tables or the equivalence rules of Figure.a. Smoke ↔ Smokeb. Smoke → Firec. (Smoke → Fire) → (—Smoke → –––Fire)d. Smoke V Fire V —Firee. ((Smoke Λ Heat) →
(Adapted from Bar wise 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, hut if it is not mythical, then it is a mortal mammal. If the unicorn is either immortal or a mammal, then it is
Any propositional logic sentence is logically equivalent to the assertion that each possible world in which it would be false is not the case. From this observation, prove that any sentence can be written in CNF.
Minesweeper, the well-known computer game, is closely related to the wumpus world. A minesweeper world is a rectangular grid of N squares with M invisible mines scattered among them. Any square may be probed by the agent; instant death follows if a mine is probed. Minesweeper indicates the presence
This exercise looks into the relationship between clauses and implication sentences.a. Show that the clause (—P1 V . . . V —Pm VQ) iS logically equivalent to the implication sentence (P1 Λ . . . Λ Pm) Q.b. Show that every clause (regardless of the number of positive literals) can be written
In this exercise, you will design more of the circuit-based wumpus agent.a. Write an equation, similar to Equation (7.4), for the Arrow proposition, which should be true when the agent still has an arrow. Draw the corresponding circuit.b. Repeat part (a) for Facing Right, using Equation (7.5) as a
Discuss what is meant by optimal behavior in the wumpus world. Show that our definition of the PL-WUMPUS-AGENT is not optimal, and suggest ways to improve it.
Extend PL-WUMPUS-AGENT so that it keeps track of all relevant facts within the knowledge base.
How long does it take to prove KB | = α using DPLL when α is a literal already contained in KB? Explain.
A logical knowledge base represents the world using a set of sentences with no explicit structure. An analogical representation, on the other hand, has physical structure that corresponds directly to the structure of the thing represented. Consider a road map of your country as an analogical
Consider a knowledge base containing just two sentences: P(α) and P(h). Does this knowledge base entail V x P(x)? Explain your answer in terms of models.
Is the sentence Э x, y x = y valid? Explain.
Write down a logical sentence such that every world in which it is true contains exactly one object.
Consider a symbol vocabulary that contains c constant symbols, predicate symbols of each arity k, and fk function symbols of each arity k, where 1 ≤ k ≤ A. Let the domain size be fixed at D. For any given interpretation—model combination, each predicate or function symbol is mapped onto a
Represent the following sentences in first-order logic, using a consistent vocabulary (which you must define):a. Some students took French in spring 2001.b. Every student who takes French passes it.c. Only one student took Greek in spring 2001.d. The best score in Greek is always higher than the

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Artificial Intelligence A Modern Approach 2nd Edition Stuart J. Russell and Peter Norvig - Solutions

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