CSU 670 Review

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CSU 670 Review

• Fall 2008

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Software Development

• Application area robotic games based on
  combinatorial maximization problems.
• Software development is about collecting enough
  knowledge about the application area and
  communicating this knowledge to the machine.
• SOFTWARE DEVELOPMENT requires application experts
  and design/programming experts. Software
  developers need to talk the language of
  application experts.

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Our Application Area

• Was chosen carefully to learn more about CS core
  topics algorithms, complexity, optimization of
  continuous and discrete functions, discrete
  mathematics, a bit of game theory.

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Application Area SDG

• Classic Specker Derivative Game with potential
  option to extend for the Secret SDG.
• Two interpretations
• Trading financial derivatives
• Create a new world of organisms in which they
  need to survive by trading with each other
  intelligently. (a small model of what humans do.)

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SDG game Classic

• Generic version derivatives, predicates, raw
  materials, finished products.
• Specialized version choose MAX-CSP as substrate.
  Predicates choose subsets of MAX-CSP instances.
  E.g., the MAX-CSP instances that only use (22).
  raw materials CSP formulae. finished product
  raw material assignment.

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Flow of one match(reusing chess terminology)

• The game is a sequence of moves by two players,
  called White (W) and Black (B).
• A move consists of two mini moves
• W offers B buys or reoffers if buy, W delivers
  raw material B finishes.
• the same but W and B swapped.
• The number of moves is predetermined.
• Winner most money, gets 1 point. If same amount
  draw (½ point).

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SDG game Secret

• Generic version derivatives, predicates, raw
  materials (hide secret), finished products
  (attempt to reveal secret).
• Specialized version choose MAX-CSP, or other
  combinatorial maximization problem, as substrate.
  Predicates choose subsets of instances. raw
  materials instance quality of secret
  solution. finished product raw material
  solution coming close to secret solution.

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Secret SDG Game

• About finding subsets of NP-hard maximization
  problems that can be solved or approximated
  efficiently.
• Predicate of the derivative defines the subset.

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Example of secret derivative

• 4 coloring of graphs.
• As CSP problem Encode 4 colors with 2 bits. Need
  one relation of arity 4 and one constraint per
  edge.
• Constraint for edge (x,y) COLOR(x1,x2,y1,y2) !
  ((x1,x2) (y1,y2))
• Predicate Graph is planar can be embedded in
  plane.
• derivative (COLOR planar, price ??)

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Four Color Conjecture(England, middle of 19th
century)

• Every planar graph can be colored with 4 colors.
• Became Four Color Theorem in 1976 by Appel and
  Haken.
• Proof is a simple induction on the number of
  regions but the induction step requires nearly
  2000 complicated cases. Only a computer can check
  that.
• What should the price be for (COLOR planar, price
  ??)

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Another secret example

• derivative d ((22),p)
• we know that we can find efficiently a solution
  that is at least 4/9 the maximum.
• derivative d ((22),4/9) we would buy.
• The raw material might now be a satisfiable
  formula in a symmetric formula we could achieve
  the maximum in polynomial time.
• Maybe there is a better polynomial approximation
  algorithm that achieves 4/9 epsilon of the
  maximum. An open problem.

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Software Development

• Complexity of application area needs to be
  interesting but not too hard only basic skills
  should be required. SDG satisfies that.
• Interesting application area leads to appropriate
  challenges for software developers.

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Challenges

• What are the requirements?
• Win at selling and buying derivatives.
• Architecture of player and administrator.
• Review Pragmatic Programmer Tips
• Write Code That Writes Code
• Use Assertions to Prevent the Impossible
• Configure, Dont Integrate
• Estimate the Order of your Algorithms

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More tips

• Refactor Early, Refactor Often
• Test Your Software, or Your Users Will