Uninformed Search R N Chapter 3 State Space

Uninformed Search R & N Chapter 3

State Space Search We need: • Set of states • A start state • A set of operators (a successor function), possibly with costs attached. • A set of goal states (or a way to test for goal)

A Water Jug Problem You are given two jugs, a 4 -gallon one and a 3 -gallon one. Neither has any measuring markers on it. There is a pump that can be used to fill the jugs with water. How can you get exactly 2 gallons of water into the 4 -gallon jug? States: Start state: Operators: Goal state:

School Lunch Planning States: Start state: Operators: Goal state:

Criminal Defense Lawyer States: Start state: Operators: Goal state:

Incremental vs. Complete State Formulation 8 -Queens States: Start state: Operators: Goal state:

Search Two key decisions: • Use a tree or a graph • How to choose which node to expand next Example:

Performance Criteria • Completeness • Optimality • How good is the solution? (R & N call this optimality) • How efficient is the search algorithm at finding the solution? (R & N call this Time and Space complexity)

The Outline of a Basic Tree Search

Breadth-First Search Is this a good idea?

Breadth-First Search – When to Evaluate?

Depth-First Search

The British Museum Algorithm A simple algorithm: Generate and test When done systematically, it is basic depth-first search. But suppose that each time we end a path, we start over at the top and choose the next path randomly. If we try this long enough, we may eventually hit a solution. We’ll call this The British Museum Algorithm or The Monkeys and Typewriters Algorithm http: //www. arn. org/docs 2/news/monkeysandtypewriters 051103. htm

Iterative Deepening

Is Iterative Deepening a Win? N(BFS) = b + b 2 + … + bd + (bd+1 -b) This last term is because of how R&N define best-first search. N(IDS) = (d)b + (d-1)b 2 + … + (1)bd Example: Let b = 10 and d = 5: N(IDS) = 50 + 400 + 3, 000 + 20, 000 + 100, 000 = 123, 450 N(BFS) = 10 + 100 + 1, 000 + 100, 000 + 999, 990 = 1, 111, 100 But there is a real saving in memory.

Is ID a Win? The Mathematics Breadth-first search: Iterative deepening: Lower bound: Upper bound:

Is Iterative Deepening a Win?

Which Direction Should We Search? Our choices: Forward, backwards, or bidirectional The issues: How many start and goal states are there? Branching factors in each direction How much work is it to compare states?

Tree or Graph? Issues: How common are repeated states? How expensive is it to compare states? Examples: 8 -puzzle chess school lunch planning defense lawyer theorem proving