1. Part2 AI as Representation and Search
Dr. Bernard Chen Ph.D.
University of Central Arkansas
Spring 2011

2. Outline Intro to Representation and Search
Ch3 Structures and strategies for state space search

3. Introduction to Representation
The representation function is to capture the critical features of a problem and make that information accessible to a problem solving procedure
Expressiveness (the result of the feature abstracted) and efficiency (the computational complexity) are major dimensions for evaluating knowledge representation

4. Introduction to Representation
The computer representation of floating-point numbers illustrate these trade-off
To be precise, real number require an infinite string of digits to be fully described.
This cannot be accomplished on a finite device such as computer

5. Introduction to Representation

6. Introduction to Representation
The array is another representation common in computer science
For many problems, it is more natural and efficient than the memory architecture implemented in computer hardware

7. Introduction to Representation

8. Introduction to Search
Given a representation, the second component of intelligent problem solving is search
Human generally consider a number of alternatives strategies on their way to solve a problem
Such as chess
Player reviews alternative moves, select the “best” move
A player can also consider a short term gain

9. Introduction to Search
Consider “tic-tac-toe”
Starting with an empty board,
The first player can place a X on any one of nine places
Each move yields a different board that will allow the opponent 8 possible responses
and so on…

10. Introduction to Search
We can represent this collection of possible moves by regarding each board as a state in a graph
The link of the graph represent legal move
The resulting structure is a state space graph

11. “tic-tac-toe” state space graph

12. Introduction to Search
Consider a task of diagnosing a mechanical fault in an automobile:

13. Introduction to Search

14. Introduction to Search
Human use intelligent search
Human do not do exhaustive search
The rules are known as heuristics, and they constitute one of the central topics of AI search

15. Outline Intro to Representation and Search
Ch3 Structures and strategies for state space search

16. State Space Representation
In the state space representation of a problem, the nodes of a graph correspond to partial problem solution states and the arcs correspond to steps in a problem solving process
One or more initial states form the root of the graph
The graph also defines one or more goal conditions, which are solutions to a problem

17. State Space Representation
State space search characterizes problem solving as the process of finding a solution path form the start state to a goal
A goal may describe a state, such as winning board in tic-tac-toe

18. “tic-tac-toe” state space graph

19. State Space Representation
In the 8-puzzle, 8 different numbered tiles are fitted into 9 spaces on a grid
One space is left blank so that tiles can be moved around to form different patterns
The goal is to find a series of moves of tiles into the blank space that places the board in a goal configuration:

20. State Space Representation
A goal in configuration in the 8-puzzle

21. State Space Representation
The Traveling salesperson problem
Suppose a salesperson has five cities to visit and then must return home
The goal of the problem is to find the shortest path for the salesperson to travel

22. State Space Representation
An instance of the traveling salesperson problem with some greedy concept

23. State Space Representation

24. State Space Representation
As previous slide suggests, the complexity of exhaustive search in the traveling salesperson problem is (N-1)!
It is a NP problem

25. Outline Strategies for state space search
Depth-First and Breadth-First Search

26. Strategies for state space search
A state may be searched in two directions:
From the given data of a problem instance toward a foal or
From a goal to the data

27. Strategies for state space search
In data driven search, also called forward chaining, the problem solver begins with the given facts of the problem and set of legal moves for changing state
This process continues until (we hope!!) it generates a path that satisfies the goal condition

28. Strategies for state space search
An alternative approach (Goal Driven) is start with the goal that we want to solve
See what rules can generate this goal and determine what conditions must be true to use them
These conditions become the new goals
Working backward through successive subgoals until (we hope again!) it work back to

29. Strategies for state space search
For example:
Consider the problem of confirming or denying the statement “I am a descendant of Thomas Jefferson”
Some facts:
He was born about 250 years ago
Assume 25 years per generation

30. Strategies for state space search
As each person has 2 parents, if we search back (goal driven) starting from “I”, the search space would be 2^10
If we assume an average of only 3 children per family, the search space for search forward (data driven) would be 3^10
Therefore, the decision to choose between data- and goal- driven search is based on the structure of the problem

31. Outline Strategies for state space search
Depth-First and Breadth-First Search

32. BFS and DFS
In addition to specifying a search direction (data-driven or goal-driven), a search algorithm must determine the order in which states are examined in the graph
Two possibilities:
Depth-first search
Breadth-first search

33. BFS and DFS
In DFS, when a state is examined, all of its children and their descendants are examined before any of its siblings
Breadth-first search explores the space in a level-by-level fashion

34. BFS and DFS

35. BFS and DFS DFS results: ABEKSLTFMCGNHOPUDIQJR
BFS results: ABCDEFGHIJKLMNOPQRSTU

36. 8-puzzle BFS

37. 8-puzzle DFS

38. BFS and DFS Properties of BFS
Because it always examines all nodes at level n before proceeding to level n+1, BFS always finds the shortest path to a goal
In a problem have a simple solution, the solution will be found
Unfortunately, if the states have a high average number of children, it may use all the memory before it find a solution

39. BFS and DFS Properties of DFS
If it is known that the solution path will be long, DFS will not spend time searching a large number of “shallow” states in the graph
However, DFS may “lost” deep in a graph, missing short paths to a goal, or even stuck in an infinite loop

40. BFS and DFS
A nice compromise on these trade-offs is to use a depth bound on DFS
New slide shows a DFS with a depth bound of 5

41. BFS and DFS

42. BFS and DFS
DFS with iterative deepening performs a DFS search of the space with a depth bound of 1,
If it fails to find a goal, it performs another DFS with depth bound of 2

43. BFS and DFS
Unfortunately, all the search strategies discussed in this chapter may be shown to have worst-case exponential time complexity
This is true for all uniformed search algorithms
Any other search algorithms???