Water Jug Problem and State Space Representation Quiz

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Questions and Answers

What is the final state in the Monkey and Banana Problem based on the provided state space representation?

  • (any other position P, any other position P, yes, yes)
  • (middle, middle, yes, no)
  • (*, *, *, yes) (correct)
  • (door, window, yes, no)

Which operator is used to move the monkey from the door to any other position in the Monkey and Banana Problem?

  • grasp
  • walk(P) (correct)
  • push(P)
  • climb

What is the initial state of the monkey in the Monkey and Banana Problem?

  • (window, door, no, no)
  • (door, window, yes, no)
  • (door, window, no, no) (correct)
  • (middle, middle, yes, no)

In the theorem proving problem, what is the user required to do with the provided axioms to find the solution?

<p>Relate them in any particular sequence (C)</p> Signup and view all the answers

Which action allows the monkey to finally grasp the banana in the Monkey and Banana Problem?

<p>grasp (D)</p> Signup and view all the answers

What represents a part of a state in the State Space Representation of the Monkey and Banana Problem?

<p>(yes, no) (C)</p> Signup and view all the answers

What does the blank square on the 8-Puzzle board represent?

<p>A space for moving tiles (B)</p> Signup and view all the answers

How is each state of the 8-Puzzle problem represented?

<p>As a 3x3 matrix with one blank tile and 7 tiles numbered (B)</p> Signup and view all the answers

What are the valid movements for the empty space in the 8-Puzzle problem?

<p>Up, Down, Right, Left (D)</p> Signup and view all the answers

In the context of 8-Puzzle, what does an initial state represent?

<p>A random arrangement of tiles at the start (C)</p> Signup and view all the answers

Which of the following is an example of an intermediate state in the 8-Puzzle problem?

<p>1 2 0 4 5 3 7 8 6 (C)</p> Signup and view all the answers

What are the valid movement directions for the empty space in the State Space Representation problem of the 8-Puzzle?

<p>Up, Down, Right, Left (C)</p> Signup and view all the answers

In the context of the water jug problem, what does the state (0,0) represent?

<p>Both jugs are empty (D)</p> Signup and view all the answers

Which rule allows pouring all the water from the 3-L jug into the 4-L jug?

<p>(x, y) → (x+y, 0) (D)</p> Signup and view all the answers

What does the rule (x, y) → (4, y - (4 - x)) represent in the water jug problem?

<p>Pouring some water from the 3-L jug to fill the 4-L jug (A)</p> Signup and view all the answers

When can we fill the 3-L jug completely based on the rules provided for the water jug problem?

<p>When x &gt; 0 (C)</p> Signup and view all the answers

Which rule describes emptying the 3-L jug on the ground if it has water?

<p>(x, y) → (0, y) (B)</p> Signup and view all the answers

What is the purpose of the state space representation in the context of solving problems like the water jug problem?

<p>To provide a visual representation of all possible states and transitions (D)</p> Signup and view all the answers

Flashcards

Final State in Monkey and Banana Problem

The final arrangement of the monkey, the banana, and the boxes in the Monkey and Banana Problem, indicating the monkey has successfully retrieved the banana.

walk(P) Operator

An action that allows the monkey to move from its current position to any other location within the room in the Monkey and Banana Problem.

Initial State in Monkey and Banana Problem

The initial configuration of the monkey and the objects in the Monkey and Banana Problem, signifying the starting point of the problem.

Axioms in Theorem Proving

The fundamental truths or principles that are given as a foundation for finding a solution in a theorem proving problem. The user must manipulate these to reach the desired conclusion.

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grasp Action

The action that allows the monkey to directly grab the banana in the Monkey and Banana Problem, signifying the solution to the problem.

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State Attribute in Monkey and Banana Problem

A pair of values, (yes, no) or (no, yes), representing a specific attribute of a state in the Monkey and Banana Problem. For example, (yes, no) could represent the monkey having the banana, but not the box.

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Blank Square in 8-Puzzle

An empty space on the 8-Puzzle board where tiles can be moved into.

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State Representation in 8-Puzzle

A 3x3 matrix representation where each cell contains a tile number (1 to 8) and the blank square is represented by 0. Each arrangement represents a possible configuration of the 8-Puzzle problem.

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Valid Movements in 8-Puzzle

The actions available to move the blank square on the 8-Puzzle board, specifically: moving the empty space up, down, left, or right.

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Initial State in 8-Puzzle

The starting arrangement of the 8-Puzzle problem, where tiles are randomly distributed on the 3x3 board.

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Intermediate State in 8-Puzzle

Any arrangement of tiles in the 8-Puzzle problem that is not the initial or final state. It represents the puzzle's state while solving it.

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Valid Movement Directions in 8-Puzzle

The actions available to move the blank square on the 8-Puzzle board. These are moving the blank space up, down, left, or right.

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State (0, 0) in Water Jug Problem

Represents the initial state of the water jugs in the Water Jug problem, denoting both jugs are empty.

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Rule (x, y) → (x+y, 0)

Rule in the Water Jug problem which allows pouring all the water from the 3-L jug into the 4-L jug.

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Rule (x, y) → (4, y - (4 - x))

A rule in the Water Jug problem that represents pouring water from the 3-L jug into the 4-L jug, until the 4-L jug is full.

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Rule for Filling the 3-L Jug

A rule in the Water Jug problem that allows filling the 3-L jug completely when it is not filled.

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Rule (x, y) → (0, y)

A rule in the Water Jug problem that allows emptying the 3-L jug if water is present.

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State Space Representation in Problem Solving

A visual representation of all possible states and transitions between those states in a problem like the Water Jug problem. It helps understand the problem's complexity and find a solution by examining the states and transitions between them.

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Study Notes

Monkey and Banana Problem

  • Final state occurs when the monkey successfully grasps the banana.
  • The operator used to move the monkey from the door to any other position is identified as the "move" action.
  • The initial state of the monkey typically begins at a defined location, often at the door or starting point.

Theorem Proving Problem

  • Users are required to manipulate provided axioms to derive logical conclusions or solutions.

8-Puzzle Problem

  • Each state in the 8-Puzzle problem is represented by a unique configuration of tiles on the board.
  • The blank square represents the empty space where a tile can move.
  • Valid movements for the empty square include sliding adjacent tiles into the empty space.
  • An initial state refers to the starting arrangement of tiles before any moves are made.
  • An intermediate state exemplifies a configuration reached after some moves have been executed.

State Space Representation of 8-Puzzle

  • Valid movement directions for the empty space include up, down, left, and right.

Water Jug Problem

  • The state (0, 0) represents both jugs being empty.
  • The rule allowing pouring all water from the 3-L jug into the 4-L jug facilitates transferring water until one jug is full or the other is empty.
  • The rule (x, y) → (4, y - (4 - x)) indicates transferring water from the 3-L jug, filling the 4-L jug to its capacity while adjusting the level in the 3-L jug accordingly.
  • The 3-L jug can be filled completely by following the rules involving pouring and refilling as needed.
  • The rule for emptying the 3-L jug involves discarding its contents onto the ground.
  • State space representation serves to outline potential states and transitions in solving problems like the water jug issue.

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