The Scientific Community Game: Education and

Innovation Through Survival in a Virtual World of Claims

The Scientific Community Game: Education and

Innovation Through Survival in a Virtual World of Claims

Karl LieberherrNortheastern University

College of Computer and Information ScienceBoston, MA

joint work with Ahmed Abdelmeged and Bryan Chadwick

Karl LieberherrNortheastern University

College of Computer and Information ScienceBoston, MA

joint work with Ahmed Abdelmeged and Bryan Chadwick

Supported by Novartis

Why Scientific Community Game(SCG)

• … motives in academic publishing: – desire for recognition and respect from the people

one regards as peers, – desire to have impact (on conclusions being

reached, on the development of the discipline, etc.), and

– desire to participate in significant knowledge-building discourse.

• e.g., Scardamalia, M., & Bereiter, C. (1994)

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SCG is Bio-inspired

• Virtual world of scholars based on natural selection– propose, oppose (refute and strengthen) claims– maximize reputation, weak scholars are removed.

• Turn problem-solving software into virtual organisms that fend for themselves and survive in a virtual world inhabited by virtual organisms created by your peers.

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SCG is a web-based implementation of Karl Popper’s science ideas

• One of the greatest philosophers of science of the 20th century.

• Falsifiability or refutability is the logical possibility that an assertion could be shown false by a particular observation or physical experiment.

• Error elimination (refutation), performs a similar function for science that natural selection performs for biological evolution.

Bionetics 2010 4from Wikipedia

Comparison

• Karl Popper: Conjectures and Refutations, 1963

• Scientific Community Game: Claims and Refutations, 2007

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Recognition in SCG

• Scholars build their reputation by proposing and opposing claims, by defending their own claims and refuting or strengthening the claims of others.

• The higher their reputation, the more recognition.

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Impact in SCG

• Second-order environment– what one scholar does in adapting, changes the

environment so that others must readapt.

• Developing novel techniques to find superior solutions, challenges others to catch up.

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Knowledge-Building Discourse in SCG

• Communication or debate.• Refutation protocol defines the structure of

the debate and who wins. Claims are defined through a refutation protocol.

• Knowledge-building:– claims that have been defended predominantly

are candidates for truth– claims that have been refuted predominantly are

probably false.Bionetics 2010 8

Goals of SCG

• Put knowledge-building discourse on the web giving participants the option to gain recognition and to have impact.

• Focus the discourse through precise definition of claims with refutation protocols.

• Make knowledge building discourse fun and educational from the high school to the advanced research level.

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SCG = Scientific Community Game = Specker Challenge Game

What do we mean by science?

• Science consists of the formulation and testing of hypotheses based on observational evidence.

• Ours: Science consists of the formulation and testing of constructive claims based on observational evidence. Construction is computable.

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What do we mean by Scientific Method

• Hypothetico-deductive method: Formulate a hypothesis in a form that could conceivably be falsified by a test on observable data.

• Ours: Formulate a constructive claim in a form that could conceivably be falsified by a test using a protocol. The refutation protocol is part of the claim to make very explicit when refutation is successful.

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Tartaglia against Fior1535

Tartaglia was famed for his algebraic solution of cubic equations which was published in Cardan's Ars Magna.

Outline

• Introduction– Popper Science, Renaissance History: Tartaglia and Fior

• Definition of SCG– Example (Highest safe rung)

• Applications: Teaching, Software Development, Research• Claims with secrets and other protocol variants• Output of SCG, Equilibrium• Advantages and Disadvantages• Conclusions

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Definition of SCG: Domain

• Problem: Set• Solution: Set• valid: relation(Problem, Solution)• quality: function(Problem, Solution)->[0..1]

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Claim(Domain)

• Problems: Powerset(Domain.Problem)• q: Quality = [0,1]• r: Resource = N+ = positive integer

Alice claims to have a technique to solve problems in Problemswith at least quality q and using at most resources r.

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makes predictionsabout the future

Implied Protocol of Claim(Domain)

• Alice claims (problems,q,r), Bob refutes• Bob provides problem prob in Claim.Problems. • Alice solves problem prob providing sol in

Domain.Solution.• check: valid(prob,sol) and quality(prob,sol)>=q and

sol.resource<=r.• sol.resource returns Alice’ resource consumption to

solve problem prob.

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Karl Popper: Only hypotheses capable of clashing with observation reports are allowed to count as scientific.

Claim

• Problems: subset of problems• quality in [0,1]

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0

1

quality(how wellproblems inProblems can be solved)

Claim

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0

1

qualitystrengthening

correct valuation

over strengthening

Bio-inspired computing: Virtual World of SCG-Avatar

• SCG-Avatar (Claim(Domain))– State: Reputation = positive rational number– Activity

• propose new claims• oppose claims of others

– refute claim(Problems, q, r)– strengthen claim(Problems, q’, r’), q’>q or r’<r

• Reputation gain: refute others’ claims and defend own claims (counter refutation attempts)

• Reputation loss: unsuccessful refutation of other’s claim and refutation of own claims

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Tournament 1. round-robin2. Swiss-style3. elimination

1. single2. double

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Summary of SCG Definitions

Domain Problem Solution valid(Problem, Solution) quality(Problem, Solution) →[0,1]

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Claim(Domain) Problems: PowerSet(Domain.Problem) q: Quality = [0,1] r: Resource = N+

Rules of the Scientific Community: propose and oppose,be an active scholar, rules for reputation accumulation.

Tournaments

Highest Safe Rung

• You are doing stress-testing on various models of glass jars to determine the height from which they can be dropped and still not break. The setup for this experiment, on a particular type of jar, is as follows.

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Highest Safe Rung

Only two identical bottles to determinehighest safe rung

Alice Bob

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You have a ladder with n rungs, and you want to find the highest rung from which you can drop a copy of the jar and not have it break. We call this the highest safe rung. You have a fixed ``budget'' of k > 0 jars.

Highest Safe Rung

Only two identical bottles to determinehighest safe rung

HSR(9,2) ≤ 4 I doubt it: refutation attempt!

Alice Bob

Alice constructsdecision tree T ofdepth 4 and gives itto Bob. He checkswhether T is valid.Bob wins if he findsa flaw.

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3

1

0

6

1 2

4

3

5

9

97

6

87

2

4

5

8

x

y z

yes no

u

highest safe rung

Highest Safe Rung Decision TreeHSR(9,2)=5

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Finding solution for HSR(n,2)

• Approximate min x in [0,n] (n/x) + x

• Exact – MaxRungs(x,y) =MaxRungs(x-1,y-1)+MaxRungs(x-1,y)– MaxRungs(x, 2) = x + MaxRungs(x – 1, 2)– MaxRungs(0, 2) = 1– Applied to HSR(9,2)

• MaxRungs(3,2) = 7 < 9• MaxRungs(4,2) = 11 > 9

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Keith Levin CS 4800 Fall 2010

MaxRungs(x,y) = the largest numberof rungs we can test with y jars andx experiments.

breaks at root does not break at root

Find minimum x, s.t. MaxRungs(x,2) > n

MaxRungs

• MaxRungs(x,y) = sum [k=0 .. y] binomial(x,k)• All paths are of length x. At most k branches

may be left branches.• Note: y = x implies MaxRungs(x,y) = 2x

meaning a complete binary tree of depth x.• Example: binomial(3,2)+binomial(3,1)+

binomial(3,0) = 7

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Formal: HSR

• Domain: – Problem: (n,k), k <= n.– Solution: Decision tree to determine highest safe

rung.– quality(problem, solution): depth of decision tree /

number of rungs– valid(problem, solution): at most k left branches, ...

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Formal: HSR

• Claim(Domain): – Alice claims ({(25,2)},9/25,5 seconds)

• {(25,2)}: set of problems (singleton)• 9/25: quality• 5 seconds: resource

• Refutation Protocol:– Bob refutes: only one problem: (25,2)– Alice: solves problem by providing decision tree t.– predicate: t is a valid decision tree for (25,2) of depth 9

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Claim involving Experiment

Claim ExperimentalTechnique(X,Y,q,r)I claim, given raw materials x in X,I can produce product y in Y of quality qand using resources at most r.

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Outline

• Introduction– Popper Science, Renaissance History: Tartaglia and Fior

• Definition of SCG– Example (Highest safe rung)

• Applications: Teaching, Software Development, Research• Claims with secrets and other protocol variants• Output of SCG, Equilibrium• Advantages and Disadvantages• Conclusions

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Applications: Software Development

• Software Development• Teaching Constructive Domains

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Gamification of Software Development etc.

• Want reliable software to solve a computational problem? Design a game where the winning team will create the software you want.

• Want to teach a STEM domain? Design a game where the winning students demonstrate superior domain knowledge.

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Doesn’t TopCoder already do this?

STEM = Science, Technology, Engineering, and Mathematics

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SCG and TopCoder

• SCG is an abstraction and generalization of what TopCoder does.

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The Traditional Approach

Solver A

Static Benchmark

Solver B

Solver C

Team A

Team B

Team C

Parameterized by the domain.

Software: Solving HSR Problem:construct decision tree of min. depth

measure how closeto minimumHSR(9,2)=4

HSR(25,2)=7

Ranking

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The Bio-Inspired Approach

Team ASolver A

prop-opp A

Team CSolver C

prop-opp C

Team BSolver B

prop-opp B

VirtualWorld

(Game)Ranking

Parameterized by the domain.

AvatarA

AvatarC

AvatarB

DynamicBenchmark

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A Virtual WorldAvatar’s View

Administrator

Avatar

Opponents’ communication,Feedback

Claims,Problems,Solutions

Results

• Problems: Benchmark output• Solutions: Software output• Claims: statements about algorithms

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What Scholars think about!

• If I propose claim C, what is the probability that– C is successfully refuted– C is successfully strengthened

• If I try to refute claim C, what is the probability that I will fail.

• If I try to strengthen claim C, what is the probability that I will fail?

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SCG = Scientific Community Game

• Make software development more scientific.• Software developers build reputation

– propose and defend claims about their software– oppose claims made by others

• refute claims• strengthen claims

• claim includes refutation protocol

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Who are Alice and Bob?

• They are avatars developed by real Alice and real Bob.

• Alice and Bob compete with 10 other avatars in a full-round robin tournament.

• Who is the winner: The avatar with the highest reputation, i.e., the avatar who has the strongest, not successfully opposed claims (like in a real scientific community).

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Why a web application with avatars? Fair Evaluation.

What is SCG(X)

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no automationhuman plays

full automationavatar plays

degree of automation used by scholar

our focus

some automationhuman plays

0 1

more applications:test constructive knowledge

transfer to reliable, efficient software

avatar Bob

Alice

Real Scholars and Avatars:Same rules

• Are encouraged to 1. propose claims that are not easily strengthened.2. offer claims that they can successfully support.3. strengthen others’ claims, if possible. 4. stay active and propose new strong claims or

oppose others’ claims.5. become famous!

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What we want

• Engage software developers– let them produce software that models an

organism that fends for itself in a real virtual world while producing the software we want. Have fun. Focus them.

– let them propose claims about the software they produce. Reward them when they

• defend their claims successfully or • oppose the claims of others successfully.

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Clear Feedback Sense of Progress

Possibility of Success

Authenticity (Facebook)

SCG

• Gamification of software development for computational problems

• A Sociotechnical System for knowledge dissemination, innovation, and integration

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Software Engineering Properties fostered by SCG

• Reliable (otherwise the avatar is removed from the game)

• Flexible, modular (otherwise the avatar cannot be easily updated between tournaments)

• Efficient (otherwise you cannot defend your claims and oppose the claims of others)

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Adaptive and Aspect-Oriented Software is relevant!

State of Avatar SCG-Avatar: Our Vision

• Companies come to SCG website and define a competition by defining a claim domain X.

• Participating teams get baby avatars generated from X that participate in daily competitions.

• Competition generates a wealth of information: educated employees, good (undefeated) software, good algorithms, good potential employees. Reward is paid to the winner.

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State of SCG-Avatar: Our Vision

• Not only companies but faculty members who want to give their students a rich learning experience for computational problem X.

• Or editors of special issues in journals who want to use a competition to get a real world comparison of all approaches to solve computational problem X.

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Avatars propose and oppose

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CA1

CA2

CA3

CA4

egoisticAlice egoistic

Bob

reputation 1000 reputation 10

CB1

CB2

opposes (1)

provides problem (2)

solves problem

not as well as she expected based on CA2 (3)WINS!LOSES

proposed claims

transfer 200

social welfare

Life of an avatar: (propose+ oppose+ provide* solve*)*

What is SCG(X)?

TeamsDesign Problem Solver

Develop SoftwareDeliver Avatar

Avatar Alice Avatar Bob

Administrator SCG police

I am the best No!!

Let’s play constructively

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TeamAlice

TeamBob

competitive / collaborative

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Avatar Alice: claim C

Avatar Bob: opposes C, refutes: providesevidence for !C

loses reputation r wins knowledge k

wins reputation r makes public knowledge k

Outline

• Introduction– Popper Science, Renaissance History: Tartaglia and Fior

• Definition of SCG– Example (Highest safe rung)

• Applications: Teaching, Software Development, Research• Claims with secrets and other protocol variants• Output of SCG, Equilibrium• Advantages and Disadvantages• Conclusions

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Protocol Variants

• secrets: approximation problems• involving trusted third party

– renaissance: exchange of problems

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Example: Triple HSR

• Alice claims ({(25,2,0), (25,2,1), (25,2,2), (25,2,3), … ,(25,2,25)},9/25, 5 seconds)

• Refutation Protocol:– Bob refutes (25,2,17)– Alice solves problems (25,2,*) by providing

decision tree to trusted third party which reveals path p from root to 17.

– predicate: p is valid and length(p) <= 9

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Highest Safe Rung

Protocol Variation Secrets

• problem has public and private part, private part is a secret solution

• predicate has secret as argument

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Protocol Variation Secret Program for SCG-Avatar

• problem has public and private part, private part is a secret solution and goes to administrator

• Alice gives her algorithm to administrator who applies it to public part of problem

• predicate has secret as argument

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Example Claims involving secrets

• My algorithm can solve more problems using resources r than your algorithm using r.

• If I create problems for you for which I have a solution, you cannot recreate or approximate the solution with quality q using resources r.

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Output and Equilibrium

• Rich tournament history• What is an equilibrium in SCG?

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Soundness Theorem

• SCG is sound: The avatar with the best algorithms / knowledge wins (there is no way to cheat)– best: within the group of participating avatars– issues:

• Does an avatar win because she is good at solving? Or good at proposing, opposing and providing? Answer: proposing, opposing and providing all reduce to solving.

04/21/23 Games for SD 60

SCG Equilibrium

• reputations of scholars are stable• the ranking of the scholars is invariant from

tournament to tournament• the science does not progress; bugs are not

fixed, no new ideas are introduced• extreme example: All scholars are perfect:

they propose optimal claims C(ps,q) that can neither be strengthened nor refuted.

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• [Scientific Innovation in X] Avatars get skills programmed into them by clever scientists in domain X. Scientists use data mining to learn from competitions and manually improve the avatars.

• [Machine Learning Innovation in X] Avatars get skills programmed into them by an avatar caregiver programmed with learning skills and data mining skills for domain X. Avatar gets updated automatically.

Survival in SCG(X)

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second-order environment!

Blame assignment

• Where is the proposer to blame?– Bad claim that is refuted.

– Bug in problem finding algorithm?

– Bug in problem solving algorithm?

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How to use SCG(X)• Company AB needs new ideas about how to

solve optimization problems in domain X.• Define claims language for X

– X-problems– claims, includes protocol

• Submit claims language definition to SCG server.

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How to use SCG(X)• Offer prize money for winner with conditions,

e.g., performance must be at least 10% higher as performance of avatar XY that AB provides.

• 10 teams from 6 countries sign up, committing to 6 competitions. Player executables become known to other players after each competition. One team from company AB.

• The SCG server sends them the basic avatar and the administrator for testing.

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How to use SCG(X)

• Game histories known to all. Data mining!• First competition is at 23.59 on day 1.

Registration starts at 18.00 on same day. The competition lasts 2.5 hours.

• Repeat on days 7, 14, … 42.• The final winner is: Team Mumbai, winning

10000 Euro. Delivers source code and design document describing winning algorithm to AB.

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Benefits for company AB of using SCG(X)

• Teams perform know-how retrieval and integration and maybe some research. – Participating teams try to find the best knowledge in

the area.– Claims language gives control!

• The non-refuted claims give hints about new X-specific knowledge.

• A well-tested solver for X-problems that integrates the current algorithmic knowledge in field X.

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Outline

• Introduction– Popper Science, Renaissance History: Tartaglia and Fior

• Definition of SCG– Example (Highest safe rung)

• Applications: Teaching, Software Development, Research• Claims with secrets and other protocol variants• Output of SCG, Equilibrium• Advantages and Disadvantages• Conclusions

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Benefits/Disadvantages

• Benefits– competitive / collaborative– structured feedback, game history– Teaching– Research– Software Development

• Dynamic testing and evaluation

• Disadvantages– addictive

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Disadvantages of SCG

• The game is addictive. After Bob having spent 4 hours to fix his avatar and still losing against Alice, Bob really wants to know why!

• Overhead to learn to define and participate in competitions.

• The administrator for SCG(X) must perfectly supervise the game. Includes checking the legality of X-problems.– if admin does not, cheap play is possible– watching over the admin

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How to compensatefor those disadvantages

• Warn the scholars.• Use a gentleman’s security policy: report

administrator problems, don’t exploit them to win.

• Occasionally have a non-counting “attack the administrator” competitions to find vulnerabilities in administrator.– both generic as well as X-specific vulnerabilities.

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Benefits of SCG

• Social Welfare – Supported knowledge

• Claims are refuted and strengthened.• Better supported knowledge comes from better

algorithms and software.72Bionetics 2010

Advantage: Democratic

• Problem to be solved: Develop the best practical algorithms for solving computational problems in domain X.

• Issue: There are probably hundreds of papers on the topic with isolated implementations. What are the best practical algorithms?

• Our solution: Use the scientific community game SCG(X) with a suitably designed claims language to compare the software. The winning avatar has the best practical algorithms/software.

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Experience with MAX-CSP

• MAX-CSP Problem Decompositions• T-Ball (one relation), Softball (several

relations, one implication tree), Baseball (several relations).

• ALL, SECRET

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Stages for SECRET T-Ball

• MAXCUT – R(x,y)= x!=y– fair coin ½ – maximally biased coin ½ – semi-definite programming / eigenvalue

minimization 0.878

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Stages for SECRET T-Ball

• One-in-three– R(x,y,z) = (x+y+z=1)– fair coin: 0.375– optimally biased coin: 0.444

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Stages for ALL Baseball

• Propose/Oppose/Provide/Solve – based on fair coin– optimally biased coin

• correctly optimize polynomials

– correctly eliminate noise relations– correctly implement weights– …

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References

• Karl Popper, Conjectures and Refutations, London: Routledge (1963).

• Scardamalia, M., & Bereiter, C. (1994). Computer support for knowledge-building communities. The Journal of the Learning Sciences, 3(3), 265-283.

• Renaissance: Tartaglia and Fior challenge (1535).

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Conclusions• To address a computational problem domain X:

– “map it to second life”: define a scientific community game for X on the web: SCG(X)

– let the game SCG(X) run a few times and choose the winner; use strongest unrefuted claims.

• Benefits– Evaluates fairly, frequently, constructively and

dynamically. Encourages retrieval of state-of-the-art know-how, integration and discovery.

– Challenges humans, drives innovation, both competitive and collaborative.

– Avatars point humans to what needs attention in problem solution / software.

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Conclusions

• Broad applicability, e.g.,• SCG(X) provides a learning process for any

constructive domain. • Benefits

– Social Engineering: makes it fun through game.– Fair: Only hard work makes you win.– Engage a large community on one domain X.

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Thank You

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Title

• The Scientific Community Game: Education and Innovation Through Survival in a Virtual World of Claims

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Abstract• The Scientific Community Game (SCG) is a generic game for constructive domains

where claims are defined by interactive protocols. As a starter, this includes mathematical claims containing alternating quantifiers but also non-mathematical claims involving the interaction between two parties. Scholars in SCG propose and oppose claims. Opposition means refutation or, strengthening followed by refutation. The winning scholars are good at proposing strong, un-refutable claims and at spotting refutable claims of other scholars. Scholars collaborate through competition. Applications include teaching constructive topics such as calculus and algorithms.

• An especially interesting version of SCG is Avatar SCG where the scholars are implemented in software. Avatar SCG is a web application implementing competitions between hundreds of avatars spread over the web.

– Applications of Avatar SCG include:• distributed software development for computational problems• distributed knowledge maintenance and integration for computational problems• teaching software development skills

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Extra

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• 1st International ICST Conference on Theory and Practice of Algorithms in (Computer) Systems,

• 18-20 April 2011 - Rome, Italy• experimental analysis of algorithms

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Formal: Pair HSR

• Alice claims ({(25,2)},9/25)• {(25,2)}: set of problems• 9/25: quality• Refutation Protocol:

– Bob refutes: only one problem: (25,2)– Alice: solves problem by providing decision tree t.– predicate: t is a correct decision tree for (25,2) of

depth 9.

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Domain

• Problem: Set• Solution: Set• valid: relation(Problem, Solution)• quality: function(Problem, Solution)->[0..1]

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Claim(Domain)

• Problems: Powerset(Domain.Problem)• q: Quality = [0,1]• r: Resource = N+ = positive integer (optional)

Alice claims to have a technique to solve problems in Problemswith at least quality q and using at most resources r.

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Implied Protocol of Claim(Domain)

• Alice claims (problems,q,r), Bob refutes• Bob provides problem prob in Claim.Problems. • Alice solves problem prob providing sol in

Domain.Solution.• check: valid(prob,sol) and quality(prob,sol)>=q and

sol.resource<=r.• sol.resource returns Alice’ resource consumption to

solve problem prob.

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Benefit of a game SCG-Avatar(Claim(Domain))

• Knowledge discovery and evaluation– If a claim was attacked 1000 times and refuted

only twice, it is a reasonable candidate for truth.– Depends on strength of avatars: Can they defend

true claims? Can they refute wrong claims?

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Game kinds

• 2-player game– used in tournament (full round robin or Swiss

style)

• n-player game

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Data produced by a game SCG-Avatar(Claim(Domain))

• Ranking of avatars• History: data exchanged through refutation

protocols, claims proposed and strengthened• A claim strengthened must be opposed by

original proposer.• Data mining of history

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Two modes

• Teaching– give warning if

• true claim is refuted• false claim is supported

• Research– don’t know the true and false claims

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Reflection 2

• Claim: For all NPO optimization problem P, there exists an SCG-Avatar game G:– better than putting 20 people into a room– learn more (give them a test)– have more fun

• Refutation protocol:

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Reflection 1

• For all constructive domains X, there exists a SCG game G=SCG(X):– if there is at least one good scholar, the

participating scholars compared to when they cooperate in a non-structured way:

• create more knowledge about X using G, given the same amount of time, because they stay focused on X.

• have more fun thanks to the competition and collaboration.

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Reflection 3

• For all challenging constructive domain X teaching tasks, there exists an SCG family game G for X– students learn more

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Reflection Software Development

• Software Development Process based on SCG

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The Traditional Approach

Solver A

Static Benchmark

Solver B

Solver C

Team A

Team B

Team C

Parameterized by the domain.

Software: Solving HSR Problem:construct decision tree of min. depth

measure how closeto minimumHSR(9,2)=4

HSR(25,2)=7

Ranking

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The Bio-Inspired Approach

Team ASolver A

prop-opp A

Team CSolver C

prop-opp C

Team BSolver B

prop-opp B

VirtualWorld

(Game)Ranking

Parameterized by the domain.

AvatarA

AvatarC

AvatarB

DynamicBenchmark

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A Virtual WorldAvatar’s View

Administrator

Avatar

Opponents’ communication,Feedback

Claims,Problems,Solutions

Results

• Problems: Benchmark output• Solutions: Software output• Claims: statements about algorithms

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What Scholars think about!

• If I propose claim C, what is the probability that– C is successfully refuted– C is successfully strengthened

• If I try to refute claim C, what is the probability that I will fail.

• If I try to strengthen claim C, what is the probability that I will fail?

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Best response dynamicsNash Equilibria

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Highest Safe Rung

• You are doing stress-testing on various models of glass jars to determine the height from which they can be dropped and still not break. The setup for this experiment, on a particular type of jar, is as follows.

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Highest Safe Rung

Only two identical bottles to determinehighest safe rung

Alice Bob

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You have a ladder with n rungs, and you want to find the highest rung from which you can drop a copy of the jar and not have it break. We call this the highest safe rung. You have a fixed ``budget'' of k > 0 jars.

Highest Safe Rung

Only two identical bottles to determinehighest safe rung

HSR(9,2) ≤ 4 I doubt it: refutation attempt!

Alice Bob

Alice constructsdecision tree T ofdepth 4 and gives itto Bob. He checkswhether T is correct.Bob wins if he findsa flaw.

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3

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x

y z

yes no

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highest safe rung

Highest Safe Rung Decision TreeHSR(9,2)=5

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Finding solution for HSR(n,2)

• Approximate min x in [0,n] (n/x) + x

• Exact – MaxRungs(x,y) =MaxRungs(x-1,y-1)+MaxRungs(x-1,y)– MaxRungs(x, 2) = x + MaxRungs(x – 1, 2)– MaxRungs(0, 2) = 1– Applied to HSR(9,2)

• MaxRungs(3,2) = 7 < 9• MaxRungs(4,2) = 11 > 9

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Keith Levin CS 4800 Fall 2010

MaxRungs(x,y) = the largest numberof rungs we can test with y jars andat most x experiments.

breaks at root does not break at root

2

1

0

4

3

2

4

1

3

x

y z

yes no

u

highest safe rung,leaf

Highest Safe Rung Decision TreeHSR(4,2)=3

(2 y (1 y h 0 h 1) n (4 y (3 y h 2 n h 3) n h 4))Properties of decision tree:

1. at most two yes from root to any leaf.2. longest root-leaf path has 3 edges.3. each rung 1..n appears exactly once as internal node of the tree.4. each rung 0..n appears exactly once as a leaf.

root

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2

1

0

4

3

2

4

1

3

x

y z

yes no

u

root

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x

y z

yes no

u

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Swiss Tournament 1. round-robin2. Swiss-style3. elimination

1. single2. double

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The smallplayer canwin unexpectedly.

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Elimination Tournament

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Claim involving Experiment

Claim ExperimentalTechnique(X,Y,q,r)I claim, given raw materials x in X,I can produce product y in Y of quality qand using resources r.

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Why Scientific Community Game

• … motives in academic publishing: – desire for recognition and respect from the people

one regards as peers, – desire to have impact (on conclusions being

reached, on the development of the discipline, etc.), and

– desire to participate in significant knowledge-building discourse .

• e.g., Scardamalia, M., & Bereiter, C. (1994)

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Recognition in SCG

• Scholars build their reputation by proposing and opposing claims, by defending their own claims and refuting or strengthening the claims of others.

• The higher their reputation, the more recognition.

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Impact in SCG

• second-order environment– what one scholar does in adapting changes the

environment so that others must readapt.

• Developing novel techniques to find superior solutions challenges others to catch up.

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Knowledge-Building Discourse in SCG

• communication or debate.• Refutation protocol defines the structure of

the debate and who wins. Claims are defined through a refutation protocol.

• Knowledge-building:– claims that have been defended predominantly

are candidates for truth

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Bereiter & Scardamaglia

• Scardamalia, M., & Bereiter, C. (1994). Computer support for knowledge-building communities. The Journal of the Learning Sciences, 3(3), 265-283.

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Discourse

• We have roughly divided characteristics for knowledge-building discourse into three categories: – focus on problems and depth of understanding; – decentralized, open knowledge environments for

collective understanding; and – productive interaction within broadly conceived

knowledge-building communities.

• Scardamalia, M., & Bereiter, C. (1994)Bionetics 2010 120

SCG Equilibrium

• reputations of scholars are stable• the ranking of the scholars is invariant from

tournament to tournament• the science does not progress; bugs are not

fixed, no new ideas are introduced• example: All scholars are perfect: they

propose optimal claims C(ps,q) that can neither be strengthened nor refuted.

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Claims and Refutation Protocol

• Alice claims: I have a program that solves inputs in domain X with quality Q and resources R. – AliceClaim(X,Q,R)

• Bob is critical. He prepares an input in X and gives it to Alice who applies her program. Bob refutes AliceClaim(X,Q,R) iff Alice achieves < Q or uses > R. – Refutation protocol

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State of Avatar SCG

• Domain is hard-wired to Constraint Satisfaction Problems

• One Master student worked on making it generic but work is not complete.

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