AI Problem Representation and Solving
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AI Problem Representation and Solving

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Questions and Answers

What does an entry A[i, j] = 1 in an adjacency matrix indicate for an undirected graph?

  • Nodes i and j are not connected.
  • Nodes i and j are the same.
  • An edge exists between nodes i and j. (correct)
  • No edge exists between nodes i and j.

    • In the context of state space search, what does the set 'S' represent?

  • The initial and goal states only.
  • The set of all actions taken.
  • The set of all possible states. (correct)
  • The sequence of state transitions.

    • Which of the following is true about the representation of a directed graph's adjacency matrix?

  • Columns identify source nodes.
  • No directionality is represented.
  • Rows identify source nodes. (correct)
  • Rows identify destination nodes.

    • In a search problem, what does the initial state 's°' represent?

    <p>The starting point of the search.</p> Signup and view all the answers

    When defining a search problem in a maze, what does 'G' represent?

    <p>The goal state or exit point of the maze.</p> Signup and view all the answers

    What is the initial state in the context of an AI problem?

    <p>The configuration from which problem solving begins</p> Signup and view all the answers

    Which of the following correctly defines a search space in AI problem solving?

    <p>All actions that can be taken from one state to another</p> Signup and view all the answers

    In the representation of a search problem using a directed graph, what do the arcs represent?

    <p>The allowed actions between states</p> Signup and view all the answers

    What characteristic distinguishes a weighted graph from other types of graphs in AI?

    <p>Edges have a cost associated with them</p> Signup and view all the answers

    What structure does a path in a graph represent?

    <p>A sequence of states visited</p> Signup and view all the answers

    Which aspect is true for a connected graph?

    <p>For any pair of nodes, there is a path connecting them</p> Signup and view all the answers

    In the context of problem P defined by traveling from Arad to Bucharest, which component represents the goal state?

    <p>City Bucharest</p> Signup and view all the answers

    What describes a 'cycle' in a graph?

    <p>A closed path that returns to the original node</p> Signup and view all the answers

    What is the goal state for the disk puzzle involving three pegs?

    <p>All disks on Peg 3 in increasing order</p> Signup and view all the answers

    Which of the following describes a valid operator in the disk puzzle?

    <p>move(Disk C, Peg 1, Peg 2)</p> Signup and view all the answers

    In the provided state space representation, which location can be reached directly from location A?

    <p>C</p> Signup and view all the answers

    What is the initial state representation for the disk puzzle?

    <p>((A,B,C), (), ())</p> Signup and view all the answers

    Which of the following constraints is NOT applicable in the disk puzzle?

    <p>Disks must be moved sequentially by size</p> Signup and view all the answers

    In the context of the state space S, what best describes the relationship between locations in the operator set O?

    <p>They are linked through direct movements</p> Signup and view all the answers

    Which of the following is NOT a location found in the state space S?

    <p>K</p> Signup and view all the answers

    What is one of the first moves to reach the goal state in the example given?

    <p>Move Disk C to Peg 3</p> Signup and view all the answers

    What does the variable #mL represent in the state definition of the Missionaries and Cannibals problem?

    <p>Number of missionaries at the left side of the river</p> Signup and view all the answers

    Which of the following represents the goal state (G) in the Missionaries and Cannibals problem?

    <p>(0,0,2,2,1)</p> Signup and view all the answers

    In the Missionaries and Cannibals problem, which condition must be met regarding the cannibals and missionaries?

    <p>The group of cannibals cannot outnumber the group of missionaries.</p> Signup and view all the answers

    What is the maximum number of people that can be in the boat at one time according to the Missionaries and Cannibals rules?

    <p>Two</p> Signup and view all the answers

    What does the state representation (2,2,0,0,0) specifically indicate in the context of the problem?

    <p>2 missionaries on the left and 2 cannibals on the left with the boat at the left side</p> Signup and view all the answers

    Which of the following actions is NOT a valid operator in the Missionaries and Cannibals problem?

    <p>(2,1)</p> Signup and view all the answers

    What does the last bit in the state representation denote?

    <p>The location of the boat</p> Signup and view all the answers

    In the context of searching in a puzzle space, what is represented by S°?

    <p>The initial state of the puzzle</p> Signup and view all the answers

    Study Notes

    AI Problem Representation

    • An AI problem has an initial configuration called the initial state represented by (s°) and the goal state (G).
    • To solve an AI problem, you start from the initial state and apply actions to reach the goal state.
    • Actions transform the current state into a new state, moving progressively towards the goal state.

    Problem Solving in AI

    • Problem solving in AI involves finding a path from the initial state to the goal state within the search space.
    • The search space encompasses all possible states and actions that can be applied to each state.
    • Problem solving can be visualized as a graph, where nodes represent states and edges represent actions.

    Graph & Tree Representation

    • A Search problem can be represented using directed graphs, undirected graphs, or weighted graphs.
    • Directed graphs represent states as nodes and actions as arcs, indicating direction.
    • Undirected graphs represent actions without a specific direction.
    • Weighted graphs represent costs associated with actions as arc weights.

    Adjacency Matrix

    • An adjacency matrix, a square matrix, can represent a graph.
    • For undirected graphs, a value of 1 in the matrix signifies the presence of an edge between nodes, while 0 represents no connection.
    • For directed graphs, rows represent source nodes, columns represent destination nodes, and the value 1 indicates an edge from source to destination.

    Example Problem Representations

    • Travel from Arad to Bucharest: The initial state is Arad, the goal state is Bucharest, and the actions are represented by roads connecting different cities.
    • Robot in a Maze: The initial state is the robot's starting position (e.g., location A), the goal state is the target position (e.g., locations G or J), the state space includes all grid locations, and actions represent movements (e.g., left, right, up, down).
    • Tower of Hanoi: The initial state represents the arrangement of disks on pegs (e.g., all disks on peg 1), the goal state represents all disks sorted on peg 3, and actions involve moving disks between pegs following specific rules.
    • Missionaries and Cannibals: The initial state represents the initial distribution of missionaries and cannibals on each side of the river and the location of the boat, the goal state represents all missionaries and cannibals on the other side of the river, and actions involve transporting people across the river in the boat with limitations on the number of people and the rule that cannibals cannot outnumber missionaries on either side.

    Representing The Search Space

    • Search problems can be represented as a tuple [S, s°, O, G].
    • S: The set of all states in the problem
    • s°: The initial state
    • O: The set of state transition operators (actions)
    • G: The set of goal states
    • This representation aims to find a series of actions to move from the initial state to a goal state.

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    Related Documents

    Chapter 2 - General Representation of AI problems.pdf

    Description

    This quiz explores the concepts of problem representation in AI, including the initial state, goal state, and the search space. It also covers the visualization of problem solving as a graph, detailing directed and undirected graphs along with their characteristics.

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