State Space Search Techniques
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State Space Search Techniques

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@ToughestNash

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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

    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</p> Signup and view all the answers

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

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

    The 8 puzzle involves arranging tiles in a linear fashion.

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

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

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

    Both jugs in the water jug problem have measurable markings.

    <p>False</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

    Lesson 3 - State Space Search (Part 1)_fa0bc691f3af29ad29a087a117a2d84c.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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