CSU 670 Review Fall 2008

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.

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.

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.)

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.

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).

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”.

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.

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 ??)

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

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.

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.

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, Don’t Integrate –Estimate the Order of your Algorithms

More tips Refactor Early, Refactor Often Test Your Software, or Your Users Will