1. Russell and Norvig: Chapter 3, Sections 3.1 – 3.3
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Russell and Norvig: Chapter 3, Sections 3.1 – 3.3

2. Problem-Solving Agent
environment
agent ?
sensors
actuators
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3. Problem-Solving Agent
environment
agent ?
sensors
actuators
Actions
Initial state
Goal test
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4. State Space and Successor Function
Actions
Initial state
Goal test
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5. Initial State Actions Initial state Goal test state space
successor function
Actions
Initial state
Goal test
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6. Goal Test Actions Initial state Goal test state space
successor function
Actions
Initial state
Goal test
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7. Example: 8-puzzle 1 2 3 4 5 6 7 8 Initial state Goal state
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8. Example: 8-puzzle 1 2 3 4 5 6 7 8
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9. Example: 8-puzzle Size of the state space = 9!/2 = 181,440
15-puzzle  .65 x 1012
24-puzzle  .5 x 1025
0.18 sec
6 days
12 billion years
10 millions states/sec
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10. Search Problem State space Initial state Successor function Goal test
Path cost
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11. Search Problem State space Initial state Successor function Goal test
each state is an abstract representation of the environment
the state space is discrete
Initial state
Successor function
Goal test
Path cost
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12. Search Problem State space Initial state: Successor function Goal test
usually the current state
sometimes one or several hypothetical states (“what if …”)
Successor function
Goal test
Path cost
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13. Search Problem State space Initial state Successor function: Goal test
[state  subset of states]
an abstract representation of the possible actions
Goal test
Path cost
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14. Search Problem State space Initial state Successor function Goal test:
usually a condition
sometimes the description of a state
Path cost
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15. Search Problem State space Initial state Successor function Goal test
Path cost:
[path  positive number]
usually, path cost = sum of step costs
e.g., number of moves of the empty tile
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16. Search of State Space
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17. Search of State Space
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18. Search State Space
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19. Search of State Space
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20. Search of State Space
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21. Search of State Space
 search tree
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22. Simple Agent Algorithm
Problem-Solving-Agent
initial-state  sense/read state
goal  select/read goal
successor  select/read action models
problem  (initial-state, goal, successor)
solution  search(problem)
perform(solution)
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23. Example: 8-queens
Place 8 queens in a chessboard so that no two queens are in the same row, column, or diagonal.
A solution
Not a solution
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24. Example: 8-queens  648 states with 8 queens Formulation #1:
States: any arrangement of
0 to 8 queens on the board
Initial state: 0 queens on the
board
Successor function: add a
queen in any square
Goal test: 8 queens on the
board, none attacked
 648 states with 8 queens
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25. Example: 8-queens  2,067 states Formulation #2:
States: any arrangement of
k = 0 to 8 queens in the k
leftmost columns with none
attacked
Initial state: 0 queens on the
board
Successor function: add a
queen to any square in the leftmost empty column such that it is not attacked
by any other queen
Goal test: 8 queens on the
 2,067 states
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26. 실제 n-queen 문제 Neural, Genetic 또는 Heuristic 방법으로 잘 해결 최악의 경우에는 처리 불가능
실제 n이 커지면 답이 매우 많으므로 간단한 Heuristics로도 답을 쉽게 찾음
따라서 n이 커도 답을 잘 찾는다고 해서 인공지능 접근방법이 문제를 해결한다는 증거는 아님
그러나 많은 실제 문제는 알고리즘에서 이야기하는 최악의 경우로는 잘 가지 않음
더구나 대부분 우리가 원하는 답은 최적이 아니라 실제 활용해서 도움이 되는, feasible solution을 원하므로 인공지능 기법이 효과적으로 이용될 수 있음
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27. Example: Robot navigation
What is the state space?
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28. Example: Robot navigation
Cost of one horizontal/vertical step = 1
Cost of one diagonal step = 2
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29. Example: Robot navigation
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30. Example: Robot navigation
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31. Example: Robot navigation
Cost of one step = ???
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32. Example: Robot navigation
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33. Example: Robot navigation
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34. Example: Robot navigation
Cost of one step: length of segment
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35. Example: Robot navigation
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36. Example: Assembly Planning
Initial state
Complex function:
it must find if a collision-free
merging motion exists
Goal state
Successor function:
Merge two subassemblies
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37. Example: Assembly Planning
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38. Example: Assembly Planning
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39. Assumptions in Basic Search
The environment is static
The environment is discretizable
The environment is observable
The actions are deterministic
 open-loop solution
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40. Search Problem Formulation
Real-world environment  Abstraction
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41. Search Problem Formulation
Real-world environment  Abstraction
Validity:
Can the solution be executed?
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42. Search Problem Formulation
Real-world environment  Abstraction
Validity:
Can the solution be executed?
Does the state space contain the solution?
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43. Search Problems

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47. Search Problem Formulation
Real-world environment  Abstraction
Validity:
Can the solution be executed?
Does the state space contain the solution?
Usefulness
Is the abstract problem easier than the real-world problem?
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48. Search Problem Formulation
Real-world environment  Abstraction
Validity:
Can the solution be executed?
Does the state space contain the solution?
Usefulness
Is the abstract problem easier than the real-world problem?
Without abstraction an agent would be swamped by the real world
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49. Search Problem Variants
One or several initial states
One or several goal states
The solution is the path or a goal node
In the 8-puzzle problem, it is the path to a goal node
In the 8-queen problem, it is a goal node
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50. Problem Variants One or several initial states
One or several goal states
The solution is the path or a goal node
Any, or the best, or all solutions
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51. Important Parameters Number of states in state space
8-puzzle  181, puzzle  .65 x puzzle  .5 x 1025
8-queens  2,057
100-queens  1052
There exist techniques to solve
N-queens problems efficiently!
Stating a problem as a search problem
is not always a good idea!
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52. Important Parameters Number of states in state space
Size of memory needed to store a state
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53. Important Parameters Number of states in state space
Size of memory needed to store a state
Running time of the successor function
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54. Applications
Route finding: airline travel, telephone/computer networks
Pipe routing, VLSI routing
Pharmaceutical drug design
Robot motion planning
Video games
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55. Interactive English tutor
Task Environment
Observable
Deterministic
Episodic
Static
Discrete
Agents
Crossword puzzle
Fully
Sequential
Single
Chess with a clock
Strategic
Semi
Multi
Poker
Partially
Backgammon
Stochastic
Taxi driving
Dynamic
Continuous
Medical diagnosis
Image-analysis
Part-picking robot
Refinery controller
Interactive English tutor
Figure Examples of task environments and their characteristics.
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56. Summary Problem-solving agent State space, successor function, search
Examples: 8-puzzle, 8-queens, route finding, robot navigation, assembly planning
Assumptions of basic search
Important parameters
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57. Future Classes Search strategies Extensions Blind strategies
Heuristic strategies
Extensions
Uncertainty in state sensing
Uncertainty action model
On-line problem solving
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