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Representation - PowerPoint PPT Presentation

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Representation. A farmer wants to move himself, a hunrgry silver fox, a hungry, fat goose, and a sack of tasty grain across a river. Unfortunately, his boat is so tiny he can move only one of his possessions across on any trip. What is he to do?. Fox, Farmer, Goose, Grain.

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  • A farmer wants to move himself, a hunrgry silver fox, a hungry, fat goose, and a sack of tasty grain across a river. Unfortunately, his boat is so tiny he can move only one of his possessions across on any trip. What is he to do?

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Fox, Farmer, Goose, Grain

  • 5 minute break for solving the problem

  • Keep track of how you solve the problem (think about how you think to solve the problem)

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  • Look at the representation in figure 2.1.

  • Graph like representation

  • Nodes: A safe distribution of entities on both banks of the river

  • Edges: connect nodes separated by a single boat trip

  • Solution: draw a line from start state to end state

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  • How many nodes?

  • How many safe nodes?

  • How many links?

  • How many legal links?

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Representation is key

  • Node/Link representation is good

  • Once represented using nodes and links, problem is simple to solve

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  • A lexical part: What symbols are allowed in your vocabulary/lexicon

  • A structural part: constraints on how symbols can be arranged

  • A procedural part: access procedures to create, modify descriptions

  • A semantic part: associates meaning with description

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Semantic Nets

  • Lexical: Nodes, links, and app-specific link labels

  • Structural: Each link connects a tail node to a head node

  • Semantic: Nodes and links denote application specific entities

  • Procedural: node, link constructors, readers/visitors to traverse the net

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Good Representations

  • Example of a good representation in object identification

  • Identify an object as belonging to a class

  • Basic Method: Describe and Match

    • Describe Object (using a “good” representation)

    • Match to library of object descriptions

    • Return closest match

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Object Identification

  • Feature based object identification

    • Feature extractor, extracts easily identifiable object features (area, perimeter, hole count, hole area, …)

    • Values of these features locate the object in an n-dimensional feature space (an object occupies a feature point in feature space)

    • Compare the distance of unknown object’s feature point to library of known (idealized) object’s feature points. The most likely identity is determined by smallest distance.

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  • Read Chapters 1 and 2

  • Assignment 1 considers Missionaries and Cannibals is available, due Feb 4.

  • Back of book contains hints

  • Need help, talk to me

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3 Missionaries 3 Cannibals

  • Three cannibals and three missionaries are standing on the west bank of a river. A boat is available that will hold either one or two people. If the missionaries are ever outnumbered -- on either bank or in the boat -- the cannibals will eat them. Your job is to design a program (come up with a representation and implement a search algorithm) that will get everyone across the river to the east bank safely.

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Burglar and combination lock

  • Generate a combination

  • Test if it opens the safe

  • Consider 6 digit combination

    • 10^6 combinations

    • 10^6/2 combinations on average to find correct combination, 3/min  16, 24 hr weeks

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Generate and Test

  • Powerful problem solving method

  • Until a satisfactory solution is found or no more solutions can be generated

    • Generate the candidate solution

    • Test the candidate solution

  • If an acceptable solution is found, announce it; otherwise announce failure

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  • Good generator – complete, nonredundant, only generates structures arising from known formula

  • Tester – Spectrogram comparator

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  • State (of a system): Description of a system that is sufficient to determine the future

  • State space: Each node denotes a state, and each link denotes a possible one-step transition from one state to another

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State Space

  • A state space is a representation

    • That is a semantic net

    • In which

      • Nodes denote states

      • Links denote transitions between states

  • Initial state, current state, goal state