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Artificial Intelligence: Foundations Of Computational Agents 3rd Edition David L. Poole , Alan K. Mackworth - Solutions
The aim of this exercise is to prove and extend the table of Figure 7.5 (page 277).(a) Prove the optimal predictions for training data of Figure 7.5. To do this, find the minimum value of the absolute error, the squared error, the log loss, and the value that gives the maximum likelihood. The
To implement the function add constraint(A0 < A1,Constraints)used in the partial-order planner, you have to choose a representation for a partial ordering. Implement the following as different representations for a partial ordering:(a) Represent a partial ordering as a set of less-than relations
Give a condition for the CSP planner that, when arc consistency with search fails at some horizon, implies there can be no solutions for any longer horizon. [Hint: Think about a very long horizon where the forward search and the backward search do not influence each other.] Implement it.
Explain how multiple-path pruning can be incorporated into a regression planner. When can a node be pruned? See the discussion, page 244.
For the delivery robot domain, give a non-trivial admissible heuristic function for the regression planner. A non-trivial heuristic function is non-zero for some nodes, and always non-negative. Does it satisfy the monotone restriction?
In a forward planner, a state can be represented in terms of the sequence of actions that lead to that state.(a) Explain how to check whether the precondition of an action is satisfied, given such a representation.(b) Explain how to do cycle pruning (page 109) in such a representation. You can
Given a STRIPS representation for actions a1 and a2, define the STRIPS representation for the composite action a1; a2, which means that the agent does a1 then does a2.(a) What are the effects for this composite action?(b) When is the composite action impossible? (That is, when is it impossible for
Suppose you must solve planning problems for cleaning a house.Various rooms can be dusted (making the room dust-free) or swept (making the room have a clean floor), but the robot can only sweep or dust a room if it is in that room. Sweeping causes a room to become dusty (i.e., not dust-free). The
This exercise involves designing a heuristic function that is better than the heuristic of Example 6.10 (page 240).(a) For each of the forward and regression planners, test how effective each of the individual parts of the heuristic for Example 6.10 is, as well as the maximum. Explain why the
Suppose the robot cannot carry both mail and coffee at the same time, but the robot can carry a box in which it can place objects (so it can carry the box and the box can hold the mail and the coffee). Suppose boxes can be picked up and dropped off at any location. Give the STRIPS representation
Change the representation of the delivery robot world of Example 6.1 (page 232) so that the robot cannot carry both mail and coffee at the same time.Test it on an example that gives a different solution than the original representation.
Consider the planning domain in Figure 6.1 (page 232).(a) Give the STRIPS representations for the pick up mail (pum) and deliver mail(dm) actions.(b) Give the feature-based representation of the MW and RHM features.
so that we can explain the possible observations no signal gc, get signal gc, or static gc? You may ignore the high-bandwidth links. You may invent any symbols you need.
(page 229).(b) Suppose that an atmospheric disturbance dist could produce static or no signal in the low-bandwidth signal. To receive the static, antenna a3 and the spacecraft’s low-bandwidth transmitter sc lg must be working. If a3 or sc lg are not working or sc is dead, there is no signal. What
Figure 5.15 (page 230) shows a simplified redundant communication network between an unmanned spacecraft (sc) and a ground control center (gc). There are two indirect high-bandwidth (high-gain) links that are relayed through satellites (s1, s2) to different ground antennae (a1, a2). Furthermore,
Suppose you are implementing a bottom-up Horn clause explanation reasoner and you want to incrementally add clauses or assumables. When a clause is added, how are the minimal explanations affected? When an assumable is added, how are the minimal explanations affected?
Consider the bottom-up negation-as-failure proof procedure of Figure 5.11 (page 212). Suppose we want to allow for incremental addition and deletion of clauses. How does C change as a clause is added? How does C change if a clause is removed?
Suppose you have a job at a company that is building online teaching tools. Because you have taken an AI course, your boss wants to know your opinion on various options under consideration.They are planning on building a tutoring system for teaching elementary physics(e.g., mechanics and
This question explores how integrity constraints and consistencybased diagnosis can be used in a purchasing agent that interacts with various information sources on the web. The purchasing agent will ask a number of the information sources for facts. However, information sources are sometimes
(page 222). A new tenant is going to sublet your home and may want to use your system to determine what may be going wrong with the plumbing (before calling you or the plumber).There are some atoms that you will know the rules for, some that the tenant will know, and some that neither will know.
You are tasked with axiomatizing the plumbing in your home and you have an axiomatization similar to that of
Consider using abductive diagnosis on the problem in the previous question, with the following elaborations.• Valves can be open or closed. Some valves may be specified as open or closed.• A valve can be ok, in which case the gas will flow if the valve is open and not if it is closed; broken,
Consider the constraint graph of Figure 4.17 with named binary constraints. r1 is a relation on A and B, which we write as r1(A, B), and similarly for the other relations. Consider solving this network using variable elimination.(a) Suppose you were to eliminate variable A. Which constraints are
Modify VE CSP to count the number of models, without enumerating them all. [Hint: You do not need to save the join of all the constraints, but instead you can pass forward the number of solutions there would be.]
Explain how arc consistency with domain splitting can be used to count the number of models. If domain splitting results in a disconnected graph, how can this be exploited by the algorithm?
Consider the constraint network in Figure 4.16 (page 175). The form of the constraints are not given, but assume the network is arc consistent and there are multiple values for each variable. Suppose one of the search algorithms has split on variable X, so X is assigned the value a.(a) Suppose the
Give the algorithm for variable elimination to return one of the models rather than all of them. How is finding one easier than finding all?
Which of the following methods can(a) determine that there is no model, if there is not one(b) find a model if one exists(c) find all models?The methods to consider are(i) arc consistency with domain splitting(ii) variable elimination(iii) stochastic local search(iv) genetic algorithms.
Consider a scheduling problem, where there are five activities to be scheduled in four time slots. Suppose we represent the activities by the variables A, B, C, D, and E, where the domain of each variable is {1, 2, 3, 4} and the constraints are A > D, D > E, C = A, C > E, C = D, B ≥ A, B = C,
(page 173).You can use the AIPython (aipython.org) code to answer this question. Start with the arc-consistent network.(a) How well does random walking work?(b) How well does iterative best improvement work?(c) How well does the combination work?(d) Which (range of) parameter settings works best?
Consider how stochastic local search can solve
For the constraints of Example 4.9 (page 132), shown in Figure 4.5(page 139), show the variables eliminated, the constraints joined, and the new constraint (as in Example 4.23 (page 145)) for the variable ordering elimination ordering A, B, C, D.
Consider the complexity for generalized arc consistency beyond the binary case considered in the text (page 140). Suppose there are n variables, c constraints, where each constraint involves k variables, and the domain of each variable is of sized. How many arcs are there? What is the worst-case
Pose and solve the crypt-arithmetic problem SEND + MORE =MONEY as a CSP. In a crypt-arithmetic problem, each letter represents a different digit, the leftmost digit cannot be zero (because then it would not be there), and the sum must be correct considering each sequence of letters as a base ten
Consider the crossword puzzles shown in Figure 4.15. The possible words for (a) are ant, big, bus, car, has, book, buys, hold, lane, year, ginger, search, symbol, syntax at, eta, be, hat, he, her, it, him, on, one, desk, dance, usage, easy, dove, first, else, loses, fuels, help, haste, given, kind,
Suppose you have a relation v(N, W) that is true if there is a vowel(one o:a, e, i, o, u) as the N-th letter of word W. For example, v(2, cat) is true because there is a vowel (“a”) as the second letter of the word “cat”; v(3, cat) is false because the third letter of “cat” is “t”,
Consider the crossword puzzle shown in Figure 4.14.You must find six three-letter words: three words read across (1-across, 4-across, 5-across) and three words read down (1-down, 2-down, 3-down). Each word must be chosen from the list of 18 possible words shown. Try to solve it yourself, first by
The depth-first branch and bound of Figure 3.14 (page 106) is like a depth-bounded search in that it only finds a solution if there is a solution with cost less than bound. Show how this can be combined with an iterative deepening search to increase the depth bound if there is no solution for a
Bidirectional search must be able to determine when the frontiers intersect. For each of the following pairs of searches, specify how to determine when the frontiers intersect:(a) breadth-first search and depth-bounded depth-first search(b) iterative deepening search and depth-bounded depth-first
The overhead for iterative deepening with b − 1 on the denominator(page 99) is not a good approximation when b ≈ 1. Give a better estimate of the complexity of iterative deepening when b ≈ 1. [Hint: Think about the case when b = 1.] How does this compare with A∗ for such graphs? Suggest a
How can depth-first branch and bound be modified to find a path with a cost that is not more than, say, 10% greater than the least-cost path. How does this algorithm compare to A∗ from the previous question?
Consider what happens if the heuristic function is not admissible, but is still non-negative. What guarantees can be made when the path found by A∗ when the heuristic function:(a) is less than 1 + times the least-cost path (e.g., is less than 10% greater than the cost of the least-cost path)(b)
The A∗ algorithm does not define what happens when multiple elements on the frontier have the same f-value. Compare the following tie-breaking conventions by first conjecturing which will work better, and then testing it on some examples. Try it on some examples where there are multiple optimal
Draw two different graphs, indicating start and goal nodes, for which forward search is better in one and backward search is better in the other.
Give two different admissible non-trivial heuristics for the video game of Example 3.3 (page 82) (depicted in Figure 3.2 (page 82)). Is one always less than or equal to the other? Explain why or why not.
This question investigates using graph searching to design video presentations. Consider a database of video segments, together with their length in seconds and the topics covered:Segment Length Topics Covered seg0 10 [welcome]seg1 30 [skiing, views]seg2 50 [welcome, artificial intelligence,
Consider the quote in Section 2.4 (page 71) from 2016: “self-driving cars . . . The technology is essentially here.” Looking back, was that an accurate assessment? Consider the subsequent development of self-driving cars and determine if that was accurate or overly optimistic. What is the
Should the owners of autonomous cars be able to select the preferences for their vehicles? Give three reasons why, and three reasons why not.Which argument do you think is more persuasive? How should the preferences of autonomous cars be determined?
Suppose you have a new job and must build a controller for an intelligent robot. You tell your bosses that you just have to implement a command function and a state transition function. They are very skeptical. Why these functions? Why only these? Explain why a controller requires a command
Suppose the robot has a battery that must be charged at a particular wall socket before it runs out. How should the robot controller be modified to allow for battery recharging?
Change the controller so that the robot senses the environment to determine the coordinates of a location. Assume that the body can provide the coordinates of a named location.
The current controller visits the locations in the to do list sequentially.(a) Change the controller so that it is opportunistic; when it selects the next location to visit, it selects the location that is closest to its current position. It should still visit all the locations.(b) Give one example
If the current target location were to be moved, the middle layer of Example 2.5 (page 62) travels to the original position of that target and does not try to go to the new position. Change the controller so that the robot can adapt to targets moving.
Consider the “robot trap” in Figure 2.11.(a) This question is to explore why it is so tricky for a robot to get to location g.Explain what the current robot does. Suppose one was to implement a robot that follows the wall using the “right-hand rule”: the robot turns left when it hits an
The obstacle avoidance implemented in Example 2.5 (page 62) can easily get stuck.(a) Show an obstacle and a target for which the robot using the controller of Example 2.5 (page 62) would not be able to get around (and will crash or loop).(b) Even without obstacles, the robot may never reach its
Consider the top-level controller of Example 2.6 (page 63).(a) If the lower level reached the timeout without getting to the target position, what does the agent do?(b) The definition of the target position means that, when the plan ends, the top level stops. This is not reasonable for the robot
The start of Section 2.2 (page 58) argued that it was impossible to build a representation of a world independently of what the agent will do with it.This exercise lets you evaluate this argument.Choose a particular world, for example, the things on top of your desk right now.(i) Get someone to
Choose four pairs of dimensions that were not compared in Section 1.5.10 (page 35). For each pair, give one commonsense example of where the dimensions interact.
For each of the Winograd schemas in Example 1.2 (page 6), what knowledge is required to correctly answer the questions? Try to find a “cheap”method to find the answer, such as by comparing the number of results in a Google search for different cases. Try this for six other Winograd schemas of
Find out about two applications of AI (not classes of applications, but specific programs). For each application, write at most one typed page describing it. You should try to cover the following questions:(a) What does the application actually do (e.g., control a spacecraft, diagnose a
Give as many disciplines as you can whose aim is to study intelligent behavior of some sort. For each discipline, find out what aspect of behavior is investigated and what tools are used to study it. Be as liberal as you can regarding what defines intelligent behavior.
For each of the following, give five reasons why:(a) A dog is more intelligent than a worm.(b) A human is more intelligent than a dog.(c) An organization is more intelligent than an individual human.Based on these, give a definition of what “more intelligent” may mean.
Ethical codes, legislation, regulation, and certification are being developed to restrict harmful applications of AI.
Transportation and sustainability are two areas of potentially beneficial applications of AI.
AI applications are permeating the economy, eliminating the need for many skills and increasing the demand for other skills.
There are concerns about the alignment between human values and AI systems, in both the short term and the long term.
Machine learning systems, trained on massive datasets, may embody racist, sexist, and other attitudes demeaning of human dignity.
The process of disintermediation, the elimination of intermediary roles, is enabled by AI. It is disruptive to employment patterns in the digital economy.
The atoms-to-bits transformation, dematerialization, and AI reduce friction in economic transactions, speeding them up.
The digital economy puts the emphasis on information rather than matter.
The recommendation systems at the heart of many large corporations are optimizing engagement, which leads to increased polarization.
Many of the probabilistic representations in earlier chapters can be made relational by including universally quantified logical variables and parameter sharing.
Plate models allow for the specification of probabilistic models before the entities are known.
Collaborative filtering and other embedding-based methods can be used to make predictions about instances of relations from other instances by inventing latent properties.
Relational representations are used when an agent requires models to be given or learned before it knows which entities it will encounter, or when the data includes identifiers (page 705), such as part numbers and booking numbers.
Data repositories with provenance, based on ontologies, are widely used in modern data-driven science.
A top-level ontology allows for a framework where domain ontologies can be designed to interoperate.
What processing has been done to the data?
What sensors were used? What is their reliability and operating range?
What were the controls? What was manipulated, when?
What was the protocol used to collect the data? Was the data chosen at random or chosen because it was interesting or some other reason?
Who transcribed the information?
Who collected each piece of data? What are their credentials?
Logic programming is useful for creating specifications, parsers, and formal scientific hypotheses.
Definite-clause grammars can be used for flexible language natural language processing in cases where the language used can be controlled, such as natural language interfaces to databases.
Game-theoretic AI can be used to model and promote prosocial environmental behavior.
For large state or action spaces, reinforcement learning algorithms can be designed to use generalizing learners such as neural networks) to represent the value function, the Q-function and/or the policy.
Utility-based decision making in the public realm can be made more transparent and accountable if the utility measures are made explicit.
Causal assumptions can be used to go beyond randomized clinical trials, if the assumptions are accepted.
Counterfactual reasoning can be used to answer “what-if” queries.
There are cases, such as in Simpson’s paradox, where the probabilistic inferences depend on the causal model and not just the data.
The do-calculus can be used to show cases where the effect of interventions can be computed from observational data, including the backdoor and front-door criteria.
D-separation characterizes which conditional independencies follow from the independencies of a directed graphical model (belief network). The do-calculus extends d-separation to include interventions.
A causal network is a belief network where P(X | parents(X)) = P(X |do(parents(X))) for each variable X – intervening on the parents of a variable has the same effect as observing them.
The do-notation extends the language of conditional probability to include intervention on some variables and observing other variables.
Bayesian techniques can help solve the practical problem of eliminating spam email.
Missing values cannot just be ignored. Why values are missing is important to be modeled and often needs to be determined from extra information.
EM and k-means are iterative methods for unsupervised learning that learn the parameters of models with hidden variables (including the case in which the classification is hidden).
Stochastic simulation is used for approximate inference.
A hidden Markov model or a dynamic belief network can be used for probabilistic reasoning about sequences, such as changes over time or words in sentences, with applications such as robot localization and extracting information from language.
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