Artificial Intelligence Structures And Strategies For Complex Problem Solving 5th Edition George F. Luger - Solutions

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Show the equivalence of the following expressions:[[∨k i=1ai] ⇒ b] ≡ [∧k i=1[ai ⇒ b]]
Show that the following expression is a tautology:[∧k i=1ai] ⇒ [∨k i=1ai]
Convert the following expression to conjunctive normal form:(a ≡ b)∨ ¬[c ∧ d]
Show that the following expression is not satisfiable:¬[(a ∧b) ⇒ a] ∧ b Construct a truth table to show that the expression is not satisfiable.
Show that the following propositional expression is a tautology:[a ⇒ b1 ∧ b2 ∧ . . . ∧ bk] ≡ [∧k i=1(a ⇒ bi)]
Construct the truth table for (a ∨ b ∨ c). Now use the truth table to create a propositional expression with seven terms. Use the laws of propositional logic to simplify this expression to (a ∨ b ∨ c).
For each of the expressions that is shown to be a tautology using the truth table method in Exercise 3, show using propositional laws that it is a tautology.
Construct the truth table for each of the following propositional expressions. Also point out if any of these expressions is a tautology:(a) (a ∧b) ⇒ a(b) (a ∨b) ⇒ a(c) a ⇒ (a ∧ b)(d) a ⇒ (a ∨ b)
Use truth tables to show that the expressions a ⇒ b and ¬b ⇒¬a are equivalent.
Show that if (¬a∨(b∧c)) and ¬b∨d each take on the value of True, then a ⇒ d must take on the value of True as well.
The previous exercise discusses the conversion of AND-OR search trees to general graphs. Discuss how you can apply AND-OR search to a general state-space graph, which is not structured as a tree. You may assume that each state includes information about which agent is making the transition. [Hint:
Consider an AND-OR tree in which alternate levels represent the moves of different players in chess. Discuss how one can compress this tree into a state-space graph, which is not necessarily structured as a tree, but has fewer nodes.
Consider a tic-tac-toe game in which the opening player puts in an ‘X’ at one of the corners and the opponent places a ‘O’ at the opposite corner. Construct the skeleton of a minimax tree (illustrating only the optimal moves for each player starting at this position) to show that the first
Implement the primitive version of the Monte Carlo tree search (which is the expected outcome model) to play a game of tic-tac-toe. Use a random move in each position for the Monte Carlo rollouts.
Discuss game situations in which minimax trees might outplay Monte Carlo trees in a game of chess for the same amount of computational power.
It is well known that playing with the white pieces has the “first-movers advantage”in chess, and very strong players of equal strength are more likely to win playing with white than when playing with black. However, it is not known whether the advantage of playing with the white pieces yields
Implement a minimax tree without alpha-beta pruning for tic-tac-toe. Now add alphabeta pruning to the program.
Consider the two-agent setting in which each agent has her own loss function. Specifically, the loss function in state i of agent A is L(i,A) and that of agent B is L(i,B).Discuss why it is possible for the agents to both cooperate and compete with the appropriate choice of loss function.
Explain how you would define the nodes of an AND-OR tree in order to handle nondeterministic environments.
Consider an AND-OR tree with five levels (including the root), where the root is an OR node, and all goal nodes are contained at the leaf level. The AND-OR tree has three branches at each node and is perfectly balanced.(a) What is the total number of leaf nodes in the tree?(b) What is the minimum
Write the pseudocode of Tabu search in which the algorithm always moves to the best possible state from each position. You can use the pseudocode of the book as a starting point.
Consider a graph a containing n nodes in which s < n nodes have been explored in the forward direction and backwards direction by bidirectional search (Figure 2.6). The graph contains a single starting state and a single goal state. What is the probability that forward search contain the single
Create a variation of best-first search in which the size of LIST is restricted by adding only the top-r successor nodes (caused by a transition from the current node) to LIST.Discuss the trade-offs associated with such a modification.
Suppose that you modify best-first search so as to restrict the number of nodes added to LIST in each iteration (cf. Figure 2.2). Discuss how restricting the number of nodes added to LIST in each iteration along with a best-first criterion provides a continuum between hill climbing and best-first
Suppose that the Boolean satisfiability problem is solved using genetic algorithms, in which the values of the variables are encoded as a string and the fitness is equal to the Boolean value of the resulting expression. Discuss why a straightforward use of genetic algorithms is unlikely to work
Express the eight-puzzle problem as a constraint satisfaction problem.
Provide the order of traversal of nodes when performing both breadth-first and depthfirst search in Figure 2.5(b). Perform tie-breaking in lexicographic order.
Modify best-first search in order to find the best alternative path from the start state to the goal state using at most d edges.
Propose a recursive algorithm for a modification of depth-first search that imposes a limit d on the depth of the search. In other words, the algorithm always backtracks when its current path from the starting state has d edges. How would you achieve this by modifying the non-recursive algorithm in
The algorithm in the text proposes a non-recursive algorithm for search. Propose a recursive algorithm for depth-first search.
Suppose that it is identified by an astute data scientist that spam emails often have the words “Free Money” embedded in them. Subsequently, the data scientist implements a system that identifies spam emails by removing all emails containing both these words.Discuss why this process involves
The solution to the eight queens problem is not unique. Provide an alternative solution to the eight queens problem beyond the one that is given in the text of the chapter.
Are the following examples of static/dynamic and discrete/continuous-time environments for the following agents: (a) A robot walking in a hallway; (b) An game of tic-tac-toe; (c) A chatbot agent talking to a person through a keyboard interface. The answers to the above might depend on the
Consider a data set of primary school students containing their date of birth, age in days, and the grade of the student. Discuss a very simple procedure for compressing the data into a single dimension, and the most likely errors resulting from such a compression.
Discuss whether each of the following agent settings below are episodic non-sequential, episodic sequential, or continuous sequential: (a) Classifying each of a set of images into one of three categories; (b) Playing a chess game; (c) Driving a car for a long time; (d) Playing a video game of
It is known from the theory of gravitation that the distance y in meters fallen by an object released from a tower with zero initial velocity is approximately given by y = 4.9x2, where x is the time in seconds. Suppose that Mr. Ignoramus, the scientist, knows nothing about the theory of
Classify each of the following as examples of either inductive learning or deductive reasoning: (a) Using a combinatorial algorithm to find the shortest path on a map from one point to another; (b) Using past experience at driving in the city to construct the shortest path from one point to
Run the ID3 algorithm in another problem domain and set of examples of your choice.
Create a CLOS simulation in another domain, e.g., an ecological scenario.
Add to the CLOS simulation of Section 16.12 a cooling system so that if any room’s temperature gets above a certain temperature it starts to cool. Also add a “thermal” factor to each room so that it heats and cools as a function of its volume and insulation value.
Write an ATN parser (Section 12.3) for a subset of English.
Extend lisp-shell to include not. For an example of how to treat negation using uncertain reasoning, refer to Chapter 8 and the PROLOG-based expert system shell in Chapter 15.
Expand the expert system shell of Section 16.10 to allow the user responses other than y or n. For example, we may want the user to be able to provide bindings for a goal. This may be done by changing ask-for and the related functions to let the user also enter a pattern, which is matched against
Select a problem such as automotive diagnosis or classifying different species of animals and solve it using lisp-shell.
Use the logic programming interpreter with arithmetic (Exercise 21) to solve the financial advisor problem of Chapter 2.
Expand the logic programming language to include arithmetic comparisons, =, .Hint: as in Exercise 20, modify solve to detect these comparisons before calling infer. If an expression is a comparison, replace any variables with their values and evaluate it. If it returns nil, solve should return the
Expand the logic programming interpreter to include LISP write statements. This will allow rules to print messages directly to the user. Hint: modify solve first to examine if a goal is a write statement. If it is, evaluate the write and return a stream containing the initial substitution set.
Rewrite the solution to the first n odd Fibonacci numbers problem so that it uses the general stream filter, filter-stream, instead of filter-odds. Modify this to return the first n even Fibonacci numbers and then modify it again to return the squares of the first n Fibonacci numbers.
Implement the general map and filter functions, map-stream and filter-stream, described in Section 16.8.
Modify the logic programming interpreter to handle or and not. Disjunctive expressions should succeed if at least one of the disjuncts succeeds; in processing a disjunctive expression, the interpreter should return the union of all the solutions returned by the disjuncts. Negation is a bit more
Rewrite print-solutions in the logic programming interpreter so that it prints the first solution and waits for a user response (such as a carriage return) before printing the second solution.
The implementations of breadth-first, depth-first, and best-first search using open and closed lists are all very similar; they differ only in the way in which open is maintained.Write a general search function that can implement any of these three searches by defining the function for maintaining
Write a LISP program to solve the full 8 × 8 version of the knight’s tour problem.
Write a LISP program to solve the 8-queens problem. (This problem is to find a way to place eight queens on a chessboard so that no queen may capture any other through a single move, i.e., no two queens are on the same row, column, or diagonal.)
Finish implementing best-first search using the general path algorithm described in Section 16.3.3. Use this along with appropriate heuristics to solve each of the three problems mentioned in Exercise 11.
Use the breadth-first search algorithm of Exercise 10 to solve:a. The farmer, wolf, goat, and cabbage problem (see Section 16.2).b. The missionary and cannibal problem (see Exercise 8).c. The water jugs problem (see Exercise 9).Compare the breadth-first results to the depth-first results. The
Implement build-solution and eliminate-duplicates for the breadth-first search algorithm of Section 16.3.
Implement a depth-first solution to the water jugs problem:There are two jugs, one holding 3 gallons and the other 5 gallons of water. A number of things that can be done with the jugs: they can be filled, emptied, and dumped one into the other either until the poured-into jug is full or until the
Implement a depth-first backtracking solution (such as was used to solve the farmer, wolf, goat, and cabbage problem in Section 16.2) to the missionary and cannibal problem:Three missionaries and three cannibals come to the bank of a river they wish to cross. There is a boat that will hold only two
Write a compiler for arithmetic expressions of the form:(op operand1 operand2)where op is either +, −, *, or / and the operands are either numbers or nested expressions.An example is (* (+ 3 6) (− 7 9)). Assume that the target machine has instructions:(move value register)(add register-1
The towers of Hanoi problem is based on the following legend:In a Far Eastern monastery, there is a puzzle consisting of three diamond needles and 64 gold disks. The disks are of graduated sizes. Initially, the disks are all stacked on a single needle in decreasing order of size. The monks are
Sets may be represented using lists. Note that these lists should not contain any duplicate elements. Write your own LISP implementations of the set operations of union, intersection, and set difference. (Do not use Common LISP’s built-in versions of these functions.)
Write the functions initialize, push, top, pop, and list-stack to maintain a global stack.These functions should behave:> (initialize)nil> (push ’foo)foo> (push ’bar)bar> (top)bar> (list-stack)(bar foo)> (pop)bar> (list-stack)(foo)
Write a random number generator in LISP. This function must maintain a global variable, seed, and return a different random number each time the function is called. For a description of a reasonable random number algorithm, consult any basic algorithms text.
a. Write a recursive LISP function that will reverse the elements of a list. (Do not use the built-in reverse function.) What is the complexity of your implementation? It is possible to reverse a list in linear time; can you do so?b. Write a LISP function that will take a list nested to any depth
Newton’s method for solving roots takes an estimate of the value of the root and tests it for accuracy. If the guess does not meet the required tolerance, it computes a new estimate and repeats. Pseudo-code for using Newton’s method to get the square root of a number is:function
Rework the semantic net parser of Section 14.3.2 to allow a richer representation of class hierarchies. Specifically, rewrite the definition of match_with_inheritance so that instead of enumerating the common specializations of two items, it computes this by searching a type hierarchy.
The simple natural language parsers presented in Section 15.9 will accept grammatically correct sentences that may not have a commonsense meaning, such as “the man bites the dog.” These sentences may be eliminated from the grammar by augmenting the parser to include some notion of what is
Explore the possibility of obtaining the probabilistic bigram values for the noun–verb, verb–object, and other word pairs of Section 15.9.3 from an actual corpus linguistics. Several of these may be found on the www.
Add probabilities for more word pair relationships as demonstrated in the lexicalized context-free parser of Section 15.9.4.
Explore the possibility of obtaining probabilities for these sentence structures from a treebank for natural language processing.Examples may be found on the www.
Extend the stochastic context-free parser of Section 15.9.3 to include appropriate probabilities for the new sentence structures built in Exercise
Write the PROLOG code for a subset of English grammar rules, as in the context-free and context-sensitive parsers found in Sections 15.9.2 and 15.9.5. Add:a. Adjectives and adverbs that can modify verbs and nouns, respectively.b. Prepositional phrases. (Can you do this with a recursive call?)c.
Build in PROLOG the ATN parser of Section 14.2.4. Add who and what questions.
Using this implementation as a reference, implement ID3 in PROLOG. Do not think of this as simply translating the LISP code to PROLOG. The languages are different and, like different natural languages, require different idioms to say the same thing. Make your PROLOG follow what you feel is a lucid
Chapter 16 presents a LISP implementation of the ID3 algorithm from Chapter
Extend the definition of ebg so that after it constructs a new rule, it asserts it to the logic database where it may be used in future queries. Test the performance of the resulting system using a theory for a suitably rich domain. You might do this by constructing a theory for a domain of your
Implement the domain theory for the float example in Chapter 10; run it with prolog_ebg.
Implement a general to specific search of the version space using the feature vector representation of Section 10.4.1. We specialize feature vectors by replacing variables with constants; since this requires telling the algorithm of allowable values for each field of the feature vector, we must
Implement a frame system with inheritance that supports the definition of three kinds of slots: properties of a class that may be inherited by subclasses, properties that are inherited by instances of the class but not by subclasses, and properties of the class and its subclasses that are not
Take the conceptual graphs used to describe the “dogs world” of Section 7.2. Translate each of the graphs used into PROLOG notation. Design PROLOG rules for the restrict, join, and simplify operations. Hint: create a list of the propositions whose conjunction make up a graph; then the
exshell allows the user to respond to queries by entering a confidence in the query’s truth, a why query, or a how query. Extend respond to allow the user to answer with y if the query is true, n if it is false. This corresponds to certainty factors of 100 and −100.
Currently, if exshell cannot solve a goal using the rule base, it fails. Extend exshell so if it cannot prove a goal using the rules, and if it is not askable, it will call that goal as a PROLOG query. Adding this option requires changes to both solve and build_proof.
Create a knowledge base in a new domain for exshell.
Fill out the rules used with the exshell cars example in the text. You might add new subsystems for the transmission or brakes.
Extend the definition of PROLOG in PROLOG (Section 15.7) to include or, and, and cut.
Create the “inventory supply” database of Section 15.6.2. Build type checks for a set of six useful queries on these data tuples.
Is the difference list catenate really a linear time append (Section 15.6)? Explain.
Create a type check that prevents the append(nil, 6, 6) anomaly.
Create the full set of ADT predicates for the priority queue in Section 15.2.
Create a triangle table-like structure to use with your planner. Use it to save, and generalize, where possible, successful move sequences.
Design a breadth-first search planner for the planner of Section 15.5. Add heuristics to the search of your planning algorithm. Can you specify a heuristic that is admissible?
Finish the code for the planner of Section 15.5. Add code for a situation that requires a new set of moves, such as adding a pyramid or sphere that could not be stacked on.
Write a PROLOG program to build the search process for the financial advisor program that was used in Chapters 2–5. Use the production system architecture. Add several more advisory rules to make the program more interesting.
Write a program to pass values up to the top level of a game tree or graph:a. Using MIN-MAX.b. Using alpha-beta pruning of the tree.c. Using both of these on the game of tic-tac-toe.
Take the path algorithm presented for the knight’s tour problem in the text. Rewrite the path call in the recursive code to the following form:path(X, Y) :- path(X, W), move(W, Y).Examine the trace of this execution and describe what is happening.
Do a to e as in Exercise 6 for the water jugs problem:There are two jugs, one holding 3 and the other 5 gallons of water. A number of things can be done with the jugs: they can be filled, emptied, and dumped one into the other either until the poured-into jug is full or until the poured-out-of jug
Do tasks a to e in Exercise 6.
Write PROLOG code to solve the full 8 × 8 knight’s tour problem. Use the production system architecture proposed in this chapter and Chapter
Use your code to check alternative forms of the missionary and cannibal problem—for example, when there are four missionaries and four cannibals and the boat holds only two.What if the boat can hold three? Try to generalize solutions for the whole class of missionary and cannibal problems.

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Artificial Intelligence Structures And Strategies For Complex Problem Solving 5th Edition George F. Luger - Solutions

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