01_State_Based_Model

Tags: #◇CSINTSY #◇Computational Thinking #◇Computer Science #◇Artificial Intelligence #◇Machine Learning #◇Intelligent Systems #◇Probability #◇Data Analysis

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◇Overview

A State-Based Model is a problem-solving approach where the world is represented as a set of states and actions that transition between them. It is...

◇Details / Theory

1. State-Based Model Reviewer

◇Overview

A State-Based Model is a problem-solving approach where the world is represented as a set of states and actions that transition between them. It is the foundation for search algorithms in Artificial Intelligence.

◇Components of a Problem

A problem is formally defined by four components:

1. Initial State ($S_0$):
   Definition: The state where the agent starts.
   Example: In a navigation app, your current location (e.g., "Campus").
   Symbol: Often denoted as $S_0$ or Start Node.

2. Actions ($A$):
   Definition: The set of available moves or operations that can be performed from a given state.
   Successor Function: A function that returns a set of (action, successor) pairs. Given a state $s$, it returns all states reachable from $s$ by a single action.
   Example: From "Campus", actions might be "Go to Street A", "Go to Street B".

3. Goal Test:
   Definition: A condition that determines if a given state is the goal state.
   Example: Is current location == "Home"?
   Symbol: Often a boolean function $IsGoal(s)$.

4. Path Cost ($g(n)$):
   Definition: A numeric cost associated with a path (sequence of actions). It is usually the sum of the costs of the individual actions (step costs).
   Step Cost: The cost of moving from state $s$ to state $s'$ via action $a$, denoted as $c(s, a, s')$.
   Optimal Solution: The solution path with the lowest path cost.

◇Key Concepts

State Space

The set of all states reachable from the initial state by any sequence of actions. It forms a graph where nodes are states and edges are actions.

Search

Definition: The process of examining different possible sequences of actions that lead to states of known value, and then choosing the best sequence. Output: A solution in the form of an action sequence (e.g., Start $\to$ A $\to$ B $\to$ Goal).

Example: N-Queens Problem

Problem: Place $n$ queens on an $n \times n$ chessboard such that no two queens attack each other. Initial State: An empty board (or a board with 0 queens). Actions: Add a queen to any square (or to the leftmost empty column) such that it is not attacked by any other queen. Goal Test: Are $n$ queens placed on the board with no attacks? Path Cost: Zero (we only care about the final state, not how we got there).

Example: Route Finding

Initial State: City A. Actions: Drive to neighboring cities. Goal Test: Are we in City B? Path Cost: Distance in kilometers or time in minutes.

◇Solved Example: Simple Graph Navigation

Consider a simple map with cities (Nodes) and roads (Edges) with distances (Costs):
S (Start) connected to A (Cost 5) and B (Cost 2). A connected to C (Cost 4). B connected to A (Cost 1) and D (Cost 6). C connected to G (Goal) (Cost 3). D connected to G (Goal) (Cost 2).

Problem: Find the path from S to G.

Step-by-Step Analysis:

1. Initial State: We are at S.
2. Possible Actions from S:
   Go to A (Cost 5). Path: $S \to A$. Total Cost: 5.
   Go to B (Cost 2). Path: $S \to B$. Total Cost: 2.
3. Exploring from B (since it's cheaper/closer):
   From B, we can go to A (Cost 1) or D (Cost 6).
   Path $S \to B \to A$: Cost $2 + 1 = 3$.
   Path $S \to B \to D$: Cost $2 + 6 = 8$.
4. Exploring from A (reached via S or B):
   From A, we can go to C (Cost 4).
   Path via S: $S \to A \to C$: Cost $5 + 4 = 9$.
   Path via B: $S \to B \to A \to C$: Cost $3 + 4 = 7$. (This is better!)
5. Exploring from C:
   From C, go to G (Cost 3).
   Path: $S \to B \to A \to C \to G$. Total Cost: $7 + 3 = 10$.
6. Exploring from D:
   From D, go to G (Cost 2).
   Path: $S \to B \to D \to G$. Total Cost: $8 + 2 = 10$.

Result: Both paths have cost 10.
Path 1: $S \to B \to A \to C \to G$ (Cost 10) Path 2: $S \to B \to D \to G$ (Cost 10)

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◇Common Pitfalls

Forgetting a component of the problem definition (initial state, actions, goal test, or path cost). Confusing the state space (all possible states) with the search tree (explored nodes during search). Not distinguishing between path cost $g(n)$ and heuristic estimate $h(n)$ — the state-based model only uses $g(n)$.

◇Summary

TL;DR — A state-based model defines AI problems as: initial state, actions (successor function), goal test, and path cost. Search algorithms explore the resulting state space to find optimal or any goal-reaching path.

◇Links

Related: Source / Reference:

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Made by 2ru17

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◇References & Navigation

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