11/11/2015SDG1 Specker Derivative Game Karl Lieberherr Spring 2009

11/11/2015SDG2 Mega moves in classic and secret SDG White-black mega move –white: offer derivatives –black: buy derivatives or reoffer –if bought then repeat r times for each bought derivative: –white: deliver raw material with witness quality(S) of secret finished product S –black: deliver finished product FP –white: reveal secret S –black: check secret S against witness quality(S) –win »classic SDG: satisfaction ratio sr(FP) wrt all. win if sr(FP) >= price * 1. »secret SDG: satisfaction ratio sr(FP) wrt secret S (think of secret S as the maximum): win if sr(FP) >= price * quality(S). –pay for performance in raw material finishing: aggregate wins

11/11/2015SDG3 derivative: (CSP predicate)

11/11/2015SDG4 SDG Game Versions T Ball (one relation) Softball –Slow Pitch (recognizing noise) one implication chain of any number of relations. –Fast Pitch any number of relations –Level k Independent (k independent relations with no implication relationship). Note: Level 1 Independent = T Ball –Level k Reduced (any number of relations that can be reduced to Level k Independent.) Note: Slow Pitch is a special case of Level 1 Reduced. Baseball –Classic and Secret CSP Any Combinatorial Maximization Problem T Ball and Softball are based on CSP

11/11/2015SDG5 SDG Game Versions T Ball Slow Pitch Fast Pitch Level k Independent Level k Reduced T Ball = Fast Pitch Level 1 Independent Slow Pitch = Special case of Fast Pitch Level 1 Reduced Softball

11/11/2015SDG6 Independent Relations Arity level 0 level 1-odd level 1-even level 3 level 2 All at level i are independent: 0 : 4 1 : 6 2: 4 Level 1-odd and 2 are also independent: 7

11/11/2015SDG7 Independent Relations Arity level 0 level 1-odd level 1-even level 3 level 2 All at level i are independent: 0 : 4 1 : 6 2: 4 Level 1-odd and 2 are also independent: 7 Red: independent set

11/11/2015SDG8 Independent Relations Arity 2 IS SEVEN THE MAXIMUM? level 0 level 1-odd level 1-even level 3 level 2 All at level i are independent: 0 : 4 1 : 6 2: 4 Level 1-odd and 2 are also independent: 7 Red: independent set

11/11/2015SDG9 Alex Lemma Consider the set of relations that are powers of 2. Alex Lemma: Any set of relations that contain exactly k relations from PT is independent. Example for arity 2: PT = { } –k=1: PT = 4 independent –k=2: = 6 independent –k=3: = 4 independent –k=4: 15 = 1 independent

11/11/2015SDG10 Implication for testing Derivative Minimizer The number of relations in the output of the minimizer must be <= MAX INDEP(3).

11/11/2015SDG11 Reliable Software Driving Artificial Worlds Reliable software is important for our society: phones, trains, cars Artificial worlds –model our own world and help to understand it better –help to teach and learn computer science software development empirical algorithmics Artificial worlds are populated by robots that must be reliable in order to survive. Survival means –following the rules of the artificial world –implement optimal trading strategies

11/11/2015SDG12 Artificial world –Definition of world: what the robots are allowed to do. create a fair world –Laws: implied by definition

11/11/2015SDG13 Combinatorial Optimization Derivatives/Raw Materials/Finished Products Combinatorial optimization problem range [0,1] Predicate language to define subsets derivative d = (pred, price) raw material r = (instance satisfying d.pred, secret finished product for r) finished product f = (r,approximation to r) quality of finished product q(f) in [0,1]

11/11/2015SDG14 Important Rules Alternating white-black/black-white mega moves. Initial life energy Life energy must stay positive Only

11/11/2015SDG15 John Pierce: instead of having artificial benchmarks use artificial markets –robots need to have both skills finding secrets hiding secrets being good at hiding secrets makes them better at finding secrets? World(Rules,Opt)

11/11/2015SDG16 Mega moves in classic and secret White-black mega move –white: offer derivatives 1<= –black: buy derivatives or reoffer –if buy derivaties then repeat r times for each bought derivative: –white: deliver raw material with witness quality(S) of secret finished product S –black: deliver finished product FP –white: reveal secret S –black: check secret S against witness quality(S) –win »classic: quality(FP). win if quality(FP) >= price. »secret SDG: quality(FP) wrt secret S (think of secret S as the maximum): win if quality(FP) >= price * quality(S). pay for performance in raw material finishing: aggregate wins –if reoffer then reoffer all derivatives on sale at a lower price Opt range [0,1] independent of CSP

11/11/2015SDG17 Mega moves in classic and secret SDG White-black mega move –white: offer derivatives –black: buy derivatives or reoffer –if buy derivaties then repeat r times for each bought derivative: –white: deliver raw material with witness quality(S) of secret finished product S –black: deliver finished product FP –white: reveal secret S –black: check secret S against witness quality(S) –win »classic: quality(FP). win if quality(FP) >= price. »secret SDG: quality(FP) wrt secret S (think of secret S as the maximum): win if quality(FP) >= price * quality(S). pay for performance in raw material finishing: aggregate wins –if reoffer then reoffer all derivatives on sale at a lower price

11/11/2015SDG18 Mega moves in classic and secret SDG White-black mega move –white: offer derivatives –black: buy derivatives or reoffer –if buy derivaties then repeat r times for each bought derivative: –white: deliver raw material with witness quality(S) of secret finished product S –black: deliver finished product FP –white: reveal secret S –black: check secret S against witness quality(S) –win »classic SDG: satisfaction ratio sr(FP) wrt all. win if sr(FP) >= price * 1. »secret SDG: satisfaction ratio sr(FP) wrt secret S (think of secret S as the maximum): win if sr(FP) >= price * quality(S). pay for performance in raw material finishing: aggregate wins –if reoffer then reoffer all derivatives on sale at a lower price

11/11/2015SDG19 SDG when CSP

11/11/2015SDG20 Mega moves in classic and secret SDG White-black mega move –white: offer derivatives –black: buy derivatives or reoffer –if buy derivatives then for each bought derivative: –white: deliver raw material with witness quality(S) of secret finished product S –black: deliver finished product FP –white: reveal secret S –black: check secret S against witness quality(S) –win »classic: quality(FP). win if quality(FP) >= price. »secret SDG: quality(FP) wrt secret S (think of secret S as the maximum): win if quality(FP) >= price * quality(S). pay for performance in raw material finishing: aggregate wins –if reoffer then reoffer all derivatives on sale at a lower price