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

04/20/23 SDG 1

Specker Derivative Game

Karl Lieberherr

Spring 2009

04/20/23 SDG 2

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

04/20/23 SDG 3

• derivative: (CSP predicate)

04/20/23 SDG 4

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 Softballare based on CSP

04/20/23 SDG 5

SDG Game Versions

T Ball

Slow Pitch

Fast Pitch

Level kIndependent

Level kReduced

T Ball = Fast Pitch Level 1 IndependentSlow Pitch = Special case of Fast Pitch Level 1 Reduced

Softball

04/20/23 SDG 6

Independent Relations Arity 2

1 2

335 9

4 8

6 10 12

7 11 13 14

15

level 0

level 1-odd

level 1-even

level 3

level 2

All at level i are independent:0 : 41 : 62: 4

Level 1-odd and 2 are also independent: 7

04/20/23 SDG 7

Independent Relations Arity 2

1 2

335 9

4 8

6 10 12

7 11 13 14

15

level 0

level 1-odd

level 1-even

level 3

level 2


Level 1-odd and 2 are also independent: 7Red: independent set

04/20/23 SDG 8

Independent Relations Arity 2IS SEVEN THE MAXIMUM?

1 2

335 9

4 8

6 10 12

7 11 13 14

15

level 0

level 1-odd

level 1-even

level 3

level 2


Level 1-odd and 2 are also independent: 7Red: independent set

04/20/23 SDG 9

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 = {1 2 4 8}– k=1: PT = 4 independent– k=2: 3 5 9 6 10 12 = 6 independent– k=3: 7 11 13 14 = 4 independent– k=4: 15 = 1 independent

04/20/23 SDG 10

Implication for testingDerivative Minimizer

• The number of relations in the output of the minimizer must be <= MAX INDEP(3).

04/20/23 SDG 11

Reliable SoftwareDriving 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

04/20/23 SDG 12

• Artificial world– Definition of world: what the robots are

allowed to do.• create a fair world

– Laws: implied by definition

04/20/23 SDG 13

Combinatorial OptimizationDerivatives/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]

04/20/23 SDG 14

Important Rules

• Alternating white-black/black-white mega moves.

• Initial life energy

• Life energy must stay positive

• Only

04/20/23 SDG 15

• 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)

04/20/23 SDG 16

Mega moves in classic and secret

• White-black mega move– white: offer derivatives 1<=– black: buy derivatives or reoffer– if buy derivaties then



» 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

04/20/23 SDG 17


• White-black mega move– white: offer derivatives– black: buy derivatives or reoffer– if buy derivaties then






04/20/23 SDG 18


• White-black mega move– white: offer derivatives– black: buy derivatives or reoffer– if buy derivaties then



» 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

04/20/23 SDG 19

• SDG when CSP

04/20/23 SDG 20


• 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





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

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