Lecture 2.1: Search Intro

Learning Objectives

• Be able to describe examples of search problems and how they are represented
• Be able to describe multiple possible state representations for a given search problem
• Practice formalizing some search problems
• Name the components of a search problem

Towers of Hanoi

Demo

State Graph

Examples of Search Problems

1. 8-Tile puzzle

2. Route-Finding

Components of a Search Problem

1. State Representation

   The state representation is how we describe the current state.

   Examples in English, Diagram, Data Structure

2. State Space

   The state space $S$ is the set of all possible states

3. Actions

   Actions are the moves available to an agent solving a search problem.

   The action space $A$ is the set of all possible moves for the search problem.

4. Transition Function

   also called “Transition Model”

   The transition function describes what happens when an action $a$ is taken from some state $s$.

   For deterministic environments (where taking the same action always leads to the same successor state), the transition function has signature $T:(S\times A)\to S$

5. Action Cost Function

   The action cost function describes the cost associated with each action.

6. Initial State

   The initial state is the state that an agent starts at when solving a search problem.

7. Goal State

   Goal states are states that an agent attempts to reach. When an agent reaches a goal state, the search problem has been completed, and a solution (a path from the initial state to the goal state) is returned.