Artificial Intelligence Goal States

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Questions and Answers

How many nodes were tested in the Uniform-Cost Search (UCS) process?

6 (correct)

What is the total cost associated with reaching node B from the starting point S?

2 (correct)

Which node has the path to the goal with the lowest cost, based on the information given?

F (correct)

From the node A, which node has the highest total cost to reach it?

D Signup and view all the answers

In the expansion of the node frontier list, which node is associated with a cost of 9?

E Signup and view all the answers

What is the main characteristic of Depth-First Search (DFS) regarding its completeness?

Fails in infinite-depth spaces. Signup and view all the answers

What modification can be made to DFS to ensure it is complete in finite spaces?

Avoid adding nodes that have already occurred on the path back to the root. Signup and view all the answers

How does the space complexity of DFS compare to the time complexity?

Space complexity is linear, whereas time complexity can be much worse. Signup and view all the answers

What happens if solutions are dense in the context of DFS?

DFS may be much faster than breadth-first search. Signup and view all the answers

Which of the following characteristics does not apply to DFS?

It guarantees the optimal solution in all scenarios. Signup and view all the answers

What is the main goal of a search in the context of state space?

To find a path from an initial state to a goal state Signup and view all the answers

Which assumption underpins state space search regarding available information?

All necessary domain information is encoded in the state description Signup and view all the answers

What does the term 'Frontier' refer to in state space search?

The states that have been generated but not yet expanded Signup and view all the answers

Which description accurately represents the 'Fringe' in tree search algorithms?

A list of nodes waiting to be expanded, sorted usually in the form of a queue Signup and view all the answers

What is a key characteristic of actions within a state space search?

Each action includes details on its legal application and resulting state Signup and view all the answers

What defines the goal in a problem formulation?

A set of goal states or a goal test Signup and view all the answers

In the context of actions required by an agent, which characteristic is NOT true?

Actions can have historical dependencies. Signup and view all the answers

Which of the following statements about the Water Jugs Problem is accurate?

The actions include filling, emptying and pouring water between pitchers. Signup and view all the answers

How is the path cost defined in a single-state problem formulation?

It is the sum of distances or number of actions executed. Signup and view all the answers

Which of the following best describes the states in the 8-Puzzle problem?

They are configurations of tiles in different arrangements. Signup and view all the answers

What must always be true for the actions defined in a problem formulation?

They should encompass all necessary changes comprehensively. Signup and view all the answers

In which scenario is a goal test considered implicit?

It involves checking a condition like 'Checkmate(x)'. Signup and view all the answers

What is meant by the term 'successor function' in problem formulation?

A function that maps current states to possible future states. Signup and view all the answers

What is a primary characteristic of bidirectional search?

It stops when the start and goal frontiers meet. Signup and view all the answers

How many nodes does bidirectional search generate compared to traditional breadth-first search?

O(bd/2) Signup and view all the answers

In which scenario might bidirectional search not be feasible?

When both directions are not breadth-first searched. Signup and view all the answers

Why might ignoring repeated states during search space traversal be problematic?

It causes unnecessary computation. Signup and view all the answers

Which search algorithm guarantees both completeness and optimality only if there is exactly one goal state?

Bidirectional search Signup and view all the answers

What is the projected performance of depth-first search in the context of tree depth?

O(b^m) in time complexity Signup and view all the answers

Which search technique could potentially run into issues with repeated states?

Both A and C Signup and view all the answers

What is one of the primary factors to consider when deciding which direction to search in a problem?

The branching factors in each direction. Signup and view all the answers

Study Notes

Goal State

Goal test can be explicitly defined, or implicitly defined by a set of goal states.
Determining the goal is typically done by the system designer or user.

Actions and Action Operators

Actions should be discrete and deterministic.
Given a specific action and the current state, the action should clearly define if it can be applied and what the next state will be.
A finite number of action operators are required.
Actions should be broken down into atomic steps.
The number of actions needed depends on how the world states are represented.

State Space Search Problem Formulation

A problem is defined by 5 key aspects:
- States: Possible configurations or positions.
- Initial State: The starting point.
- Action Function (S(x)): A function that returns the set of possible actions applied to a given state (x).
- Goal Test: A condition that checks if a state is a goal state.
- Path Cost: A value that measures the cost of a path, adding up the cost of individual actions.

Search Example: 8-Puzzle

States are represented by different configurations of the 8-puzzle.
Actions include moving the empty tile up, down, left, or right.

Water Jugs Problem

The problem is to get exactly 2 liters into the 4-liter pitcher using a 4-liter and 3-liter pitcher.
States are represented as (x, y) pairs, where x is the amount of water in the 4-liter pitcher, and y is the amount in the 3-liter pitcher.
Actions include emptying, filling, and pouring water between the pitchers.

State Space Search Assumptions

Users define the knowledge encoded in the state.
Closed World Assumption: All necessary information is provided in the state description.
Actions are assumed to be primitive, deterministic, and discrete.
The state space can be visualized as a directed graph.

Different Search Strategies

Search strategies utilize a Frontier (or Fringe) set, which contains the generated but not yet expanded states.
The choice of state to expand from the Frontier defines the search strategy.

Tree Search Algorithms

Tree search algorithms explore the state space by expanding states.
Fringe: A sorted list of nodes waiting to be expanded.
The sorting strategy of the Fringe determines how the tree is searched.

Depth-First Search (DFS)

DFS explores the depth of the tree before exploring breadth.
May not be complete in infinite-depth spaces or spaces with loops.
Time complexity: O(bm), where b is the branching factor, and m is the maximum depth.
Space complexity: O(bm).

Uniform-Cost Search (UCS)

UCS expands the node with the lowest path cost from the start node.
Guarantees finding the optimal solution (the path with the least cost).
Time complexity: O(bC*/ε), where C* is the cost of the optimal solution, and ε is the smallest possible step cost.
Space complexity: O(bC*/ε).

Bidirectional Search

Searches from both the start state and the goal state simultaneously.
Stops when the two Frontiers meet.
Time complexity: O(b^(d/2)), where d is the depth of the goal state.
Space complexity: O(bd), where d is the depth of the goal state.

Performance of Search Algorithms on Trees

Depth-First Search: Not complete, not optimal, time: O(bm), space: O(bm).
Breadth-First Search: Complete, optimal (if step costs equal), time: O(bd), space: O(bd).
Uniform-Cost Search: Complete, optimal, time: O(bC*/ε), space: O(bC*/ε).
Bidirectional Search: Complete, optimal, time: O(b^(d/2)), space: O(b^(d/2)).

Repeated States

Repeated states can occur in state spaces that are not a tree.
To avoid inefficiency, repeated states need to be handled during search.
Techniques include:
- Using an explicit data structure to store already visited nodes.
- Pruning the search tree.

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Description

This quiz explores the concept of goal states in artificial intelligence, including how they can be defined and tested. It delves into the formulation of state space search problems, discussing actions, action operators, and the requirements for problem-solving in AI. Test your understanding of these fundamental principles.