State Space Search Techniques
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Questions and Answers

What is the basic idea behind state space search?

  • To eliminate unnecessary states in a problem
  • To mentally explore possibilities before taking actions (correct)
  • To explore possibilities in a physical manner
  • To calculate the fastest route to a goal

    • An operator can take an agent from a successor state back to the initial state.

    False (B)

    What is the term used to describe the sequence of actions taken by an agent?

    plan

    The set of final states in a search problem is denoted as _____

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

    Which of the following is NOT part of a search problem?

    <p>State transition diagram (D)</p> Signup and view all the answers

    The cost of a plan in state space search is known as the path cost.

    <p>True (A)</p> Signup and view all the answers

    Define 'initial state' in the context of state space search.

    <p>The description of the starting configuration of the agent.</p> Signup and view all the answers

    Match the following terms to their definitions:

    <p>Initial State = The starting configuration of the agent Successor State = The state reached after an action has been applied Plan = A sequence of actions Path Cost = The total cost associated with a plan</p> Signup and view all the answers

    What does a search problem utilize to represent states and actions?

    <p>A directed graph (D)</p> Signup and view all the answers

    The order of operations in a search process is to check the current state, execute actions, pick a new state, and then check if it is a solution.

    <p>True (A)</p> Signup and view all the answers

    In the Pegs and Disks problem, what is the goal state for the configuration with 3 pegs and 3 disks?

    <p>All the pegs are in needle B.</p> Signup and view all the answers

    In the Tower of Hanoi problem, the initial state has all disks on needle ______.

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

    Match the following steps with their corresponding actions in the Pegs and Disks problem:

    <p>Step 1 = Move A → C Step 3 = Move A → C Step 4 = Move B → A Step 6 = Move A → B</p> Signup and view all the answers

    What is a successor state?

    <p>A state that results from executing an allowable action (B)</p> Signup and view all the answers

    In the Tower of Hanoi problem with 4 disks, all pegs should ultimately end up in needle C.

    <p>False (B)</p> Signup and view all the answers

    List one operator used in the Pegs and Disks problem.

    <p>Move the topmost disk from one needle to another.</p> Signup and view all the answers

    What is the goal test in the N queens problem formulation?

    <p>8 queens on the board with none attacking each other (A)</p> Signup and view all the answers

    The 8 puzzle involves arranging tiles in a linear fashion.

    <p>False (B)</p> Signup and view all the answers

    What is the initial state in the 8 queens problem?

    <p>All queens are at column 1</p> Signup and view all the answers

    In the N queens problem, the initial state involves _ queens on the board.

    <p>0</p> Signup and view all the answers

    Match the following problems with their correct formulations:

    <p>8 queens problem = 8 queens on the board, none attacked 8 puzzle = Tiles arranged with one blank space N queens problem = 0 to 8 queens on the board Tic-tac-toe = 3 in a row in a 3x3 grid</p> Signup and view all the answers

    What describes the successor function in the 8 puzzle?

    <p>Move the blank space left, right, up, or down (A)</p> Signup and view all the answers

    The path cost in the 8 puzzle is zero for each move.

    <p>False (B)</p> Signup and view all the answers

    What is the successor function in the N queens problem?

    <p>Add a queen in any square</p> Signup and view all the answers

    What is the initial state of the N queens problem?

    <p>All queens are at column 1 (D)</p> Signup and view all the answers

    In the water jug problem, the goal state can be represented as (2, y) where y can only be 0.

    <p>False (B)</p> Signup and view all the answers

    What representation is used to denote the state of the water jug problem?

    <p>(x, y)</p> Signup and view all the answers

    To achieve exactly 2 gallons of water in the 4-gallon jug, the initial state is ______.

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

    Match the problems with their goal state representation:

    <p>N queens problem = 8 queens on the board, none are attacked Water jug problem = (2, y) where 0 ≤ y ≤ 3</p> Signup and view all the answers

    What is the successor function in the N queens problem?

    <p>Change the position of any one queen (B)</p> Signup and view all the answers

    Both jugs in the water jug problem have measurable markings.

    <p>False (B)</p> Signup and view all the answers

    What is the maximum capacity of the 3-gallon jug in the water jug problem?

    <p>3 gallons</p> Signup and view all the answers

    Study Notes

    • Search is a general-purpose problem-solving technique.
    • Basic Idea: Before solving a problem, an agent explores all possible ways to solve it "in its head."
    • Search = (Mental) Exploration of Possibilities

    State Space Search Notations

    • Initial State: Description of the starting configuration of the agent.
    • Action (or Operator): Takes the agent from one state to another (successor state).
    • Plan: A sequence of actions.
    • Path Cost: The total cost of a plan, calculated by adding the costs of each step.

    Search Problem

    • Problem Formulation: Defining the set of states to consider and a feasible set of operators to transition between states.
    • Search: Finding a sequence of operators culminating in a goal state, starting from the initial state, by considering various possible sequences.

    Search Problem Components

    • S: The entire set of states.
    • s0: The initial state.
    • A: A set of operators that act on states and produce new states (S → S).
    • G: The set of goal states (G ⊆ S).

    Search Problem Representation

    • Directed Graph: A directed graph where:
      • Nodes: Represent states.
      • Arcs: Represent the allowed actions.

    Search Process

    • Iterative Process: Continuously repeat the following steps until a solution is found or the state space is exhausted:
        1. Check the Current State: Examine the current state.
        1. Execute Allowable Actions: Apply permissible actions to discover successor states.
        1. Pick a New State: Select one of the newly discovered successor states.
        1. Check for Solution: Determine if the selected new state is a goal state. If not, the new state becomes the current state, and the process repeats.

    Examples

    • Pegs and Disks Problem*

    • 3 pegs and 3 disks.

    • Goal: Move all disks to peg B.

    • Operators: Move the topmost disk from any peg to the topmost position on another peg.

    • 8 Queens Problem*

    • States: Any arrangement of 8 queens on a chessboard.

    • Initial State: All queens are on the first column.

    • Successor Function: Moving a queen's position.

    • Goal Test: Eight queens on the board with none attacking each other.

    • Tic-Tac-Toe*

    • States: All possible board configurations.

    • 8 Puzzle*

    • States: Each state represents a configuration of the 8 tiles within their possible locations.

    • Operators/Actions: Moving the blank space (up, down, left, right).

    • Goal Test: Reaching a predefined target state.

    • Path Cost: Each move of the blank space costs 1.

    • N Queens Problem*

    • Problem Formulation 1:

      • States: Any arrangement of 0 to 8 queens on the board.
      • Initial State: No queens on the board.
      • Successor Function: Placing a queen in any square.
      • Goal Test: 8 queens on the board with none attacking each other.

    • Problem Formulation 2:

      • States: Any arrangement of 8 queens on the board.
      • Initial State: All queens are on the first column.
      • Successor Function: Moving a queen's position.
      • Goal Test: 8 queens on the board with none attacking each other.

    • Water Jug Problem*

    • Goal: Get exactly 2 gallons of water in the 4-gallon jug.

    • State Representation: A tuple (x, y) where x is the amount of water in the 4-gallon jug and y is the amount of water in the 3-gallon jug.

    • Initial State: (0, 0)

    • Goal State: (2, y) where 0 ≤ y ≤ 3.

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    Related Documents

    Artificial Intelligence - CMPSC 162 - Lesson 3: State Space Search (Part 1) PDF

    Description

    Explore the fundamental concepts of state space search in problem-solving. This quiz covers essential notations, problem formulation, and the components of a search problem. Test your understanding of how agents transition between states and find solutions.

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