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Published byChester Campbell Modified about 1 year ago

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State Space Search Classic AI

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State Space representation of a problem is a graph Nodes correspond to problem states Arcs correspond to steps in a solution process One node corresponds to an initial state One node corresponds to a goal state

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Solution Path An ordered sequence of nodes from the initial state to the goal state

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Search Algorithm Finds a solution path through a state space

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The Water Jug Problem Suppose we have An empty 4 gallon jug An empty 3 gallon jug A source of water A task: put 2 gallons of water in the 4 gallon jug

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Representation State Space Node on the graph is an ordered pair (x,y) –X is the contents of the 4 gallon jug –Y is the contents of the 3 gallon jug Intitial State: (0,0) Goal State: (2,N) N ε {0, 1, 2, 3}

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Rules 1. if x < 4, fill x : (x,y) (4,y) 2. if y < 3, fill y : (x,y) (x,3) 3. if x > 0, empty x : (x,y) (0,y) 4. if y > 0, empty y : (x,y) (x,0) 5. if (x+y) >= 4 and y > 0 fill the 4 gallon jug from the 3 gallon jug (x,y) (4, y – (4 – x)) 6. if (x+y) >= 3 and x > 0 Fill the 3 gallon jug from the 4 gallon jug (x,y) (x –(3 – y), 3)) 7. if (x+y) 0 Pour the 3 gallon jug into the 4 gallon jug: (x,y) (x+y), 0) 8. if (x+y) 0 pour the 4 gallon jug into the 3 gallon jug: (x,y) (0, x + y)

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Is there a solution path? Initial State: (0,0) Goal State: (2,N)

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Breadth First Search (0,3) (4,0) (4,3)(1,3) (3,0) (0,3) 1 2 2 6 7 etc

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Depth First ( 3,0 ) ( 3,3 ) ( 0,3 ) ( 4,0 ) ( 4,3 ) ( 0,0 ) 1 2 3 7 2 Etc. and without visiting already visited states

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Backward/Forward Chaining Search can proceed 1. From data to goal 2. From goal to data Either could result in a successful search path, but one or the other might require examining more nodes depending on the circumstances

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Data to goal is called forward chaining for data driven search Goal to data is called backward chaining or goal driven search

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Examples Water jug was data driven Grandfather problem was goal driven To make water jug goal driven: –Begin at (2,y) –Determine how many rules could produce this goal –Follow these rules backwards to the start state

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Object Reduce the size of the search space

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Use Goal Driven if –Goal is clearly stated –Many rules match the given facts For example: the number of rules that conlude a given theorem is much smaller than the number that may be applied to the entire axiom set

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Use Data Driven If –Most data is given at the outset –Only a few ways to use the facts –Difficult to form an initial hypothesis For example: DENDRAL, an expert system that finds molecular structure of organic compounds based on spectrographic data. There are lots of final possibilities, but only a few ways to use the initial data Said another way: initial data constrains search

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