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

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

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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

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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

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Introduction to Representation

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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

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Introduction to Representation

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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

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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…

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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

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“tic-tac-toe” state space graph

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

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Introduction to Search

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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

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

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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

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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

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“tic-tac-toe” state space graph

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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:

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

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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

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

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State Space Representation

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

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

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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

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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

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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

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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

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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

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

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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

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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

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BFS and DFS

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DFS results: ABEKSLTFMCGNHOPUDIQJR BFS results: ABCDEFGHIJKLMNOPQRSTU

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8-puzzle BFS

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8-puzzle DFS

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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

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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

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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

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BFS and DFS

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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

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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???

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