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Questions and Answers
What is the basic idea behind state space search?
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.
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?
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 _____
The set of final states in a search problem is denoted as _____
Which of the following is NOT part of a search problem?
Which of the following is NOT part of a search problem?
The cost of a plan in state space search is known as the path cost.
The cost of a plan in state space search is known as the path cost.
Define 'initial state' in the context of state space search.
Define 'initial state' in the context of state space search.
Match the following terms to their definitions:
Match the following terms to their definitions:
What does a search problem utilize to represent states and actions?
What does a search problem utilize to represent states and actions?
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.
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.
In the Pegs and Disks problem, what is the goal state for the configuration with 3 pegs and 3 disks?
In the Pegs and Disks problem, what is the goal state for the configuration with 3 pegs and 3 disks?
In the Tower of Hanoi problem, the initial state has all disks on needle ______.
In the Tower of Hanoi problem, the initial state has all disks on needle ______.
Match the following steps with their corresponding actions in the Pegs and Disks problem:
Match the following steps with their corresponding actions in the Pegs and Disks problem:
What is a successor state?
What is a successor state?
In the Tower of Hanoi problem with 4 disks, all pegs should ultimately end up in needle C.
In the Tower of Hanoi problem with 4 disks, all pegs should ultimately end up in needle C.
List one operator used in the Pegs and Disks problem.
List one operator used in the Pegs and Disks problem.
What is the goal test in the N queens problem formulation?
What is the goal test in the N queens problem formulation?
The 8 puzzle involves arranging tiles in a linear fashion.
The 8 puzzle involves arranging tiles in a linear fashion.
What is the initial state in the 8 queens problem?
What is the initial state in the 8 queens problem?
In the N queens problem, the initial state involves _ queens on the board.
In the N queens problem, the initial state involves _ queens on the board.
Match the following problems with their correct formulations:
Match the following problems with their correct formulations:
What describes the successor function in the 8 puzzle?
What describes the successor function in the 8 puzzle?
The path cost in the 8 puzzle is zero for each move.
The path cost in the 8 puzzle is zero for each move.
What is the successor function in the N queens problem?
What is the successor function in the N queens problem?
What is the initial state of the N queens problem?
What is the initial state of the N queens problem?
In the water jug problem, the goal state can be represented as (2, y) where y can only be 0.
In the water jug problem, the goal state can be represented as (2, y) where y can only be 0.
What representation is used to denote the state of the water jug problem?
What representation is used to denote the state of the water jug problem?
To achieve exactly 2 gallons of water in the 4-gallon jug, the initial state is ______.
To achieve exactly 2 gallons of water in the 4-gallon jug, the initial state is ______.
Match the problems with their goal state representation:
Match the problems with their goal state representation:
What is the successor function in the N queens problem?
What is the successor function in the N queens problem?
Both jugs in the water jug problem have measurable markings.
Both jugs in the water jug problem have measurable markings.
What is the maximum capacity of the 3-gallon jug in the water jug problem?
What is the maximum capacity of the 3-gallon jug in the water jug problem?
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Study Notes
State Space Search
- 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:
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- Check the Current State: Examine the current state.
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- Execute Allowable Actions: Apply permissible actions to discover successor states.
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- Pick a New State: Select one of the newly discovered successor states.
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- 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.
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Examples
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Pegs and Disks Problem*
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3 pegs and 3 disks.
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Goal: Move all disks to peg B.
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Operators: Move the topmost disk from any peg to the topmost position on another peg.
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8 Queens Problem*
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States: Any arrangement of 8 queens on a chessboard.
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Initial State: All queens are on the first column.
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Successor Function: Moving a queen's position.
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Goal Test: Eight queens on the board with none attacking each other.
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Tic-Tac-Toe*
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States: All possible board configurations.
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8 Puzzle*
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States: Each state represents a configuration of the 8 tiles within their possible locations.
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Operators/Actions: Moving the blank space (up, down, left, right).
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Goal Test: Reaching a predefined target state.
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Path Cost: Each move of the blank space costs 1.
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N Queens Problem*
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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.
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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.
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Water Jug Problem*
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Goal: Get exactly 2 gallons of water in the 4-gallon jug.
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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.
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Initial State: (0, 0)
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Goal State: (2, y) where 0 ≤ y ≤ 3.
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