The Algorithms we use to learn about Algorithms

1. The Algorithms we use to learn about Algorithms Karl Lieberherr Ahmed Abdelmeged Open House 2011

2. Why do we model Scientific Communities? • Scientific Communities create and disseminate new knowledge to help society. • A computational model of scientific communities supports the same efforts for computational problems: • focused collaboration and competition • checking of the rules of a scientific community • knowledge maintenance and evaluation Open House 2011

3. Idea: Use Scientific Community Modelto focus scientific discourse • Scholars propose and oppose (refute or strengthen) or agree on claims. Strengthen and agree are reduced to refute. • Claims predict the outcome of a refutation protocol. • Parameterized by two structures: Domain and Protocol. • Claim Example: Alice claims that she can solve problem instances in instance set I with quality at least q using resources at most r. Open House 2011

4. Designers • SCG • Domain • Instance, Solution, InstanceSet, valid, quality • basic domain functionality, like • standard solvers and solvers for niches. • providing instances with “interesting” solutions • Protocol: using protocol language • standard protocols: ForAllExists, PositiveSecret, etc. • Playground: Configurate • Research/Development Managers (Innovation) • Professors (Teaching) • Avatar • researchers, developers • students Open House 2011

5. Confidence • Proposer of a claim attaches a confidence in [0,1] to the claim. • The scholar's confidence reflects the amount of effort made by the scholar to refute the claim. If it is a mathematical claim, it is the amount of effort spent to try to prove the claim (i.e. turning it into a theorem) Open House 2011

6. Refutation • All scholars start with same reputation. Reputation is zero sum. • Alice proposes, Bob opposes. • When scholar Bob successfully refutes a claim of Alice, Bob wins reputation: • Bob + ClaimConfidence • When scholar Alice successfully defends her own claim against Bob, Alice wins reputation. • Alice + ClaimConfidence Open House 2011

7. Strengthening • When claim C is strengthened by Bob to C', Alice must try to refute C' and the strengthening holds only if Bob defends C'. strengthenP(C,C') must hold. • When scholar Bob successfully strengthens a claim of Alice, Bob wins reputation: • Bob + ClaimConfidence + |quality(C)-quality(C')| • When scholar Alice successfully defends her own claim against Bob, Alice wins reputation. • Alice + ClaimConfidence Open House 2011

8. Agreement • When Bob agrees on claim C with Alice, • (1) Bob must defend C against Alice (if not, Bob loses ClaimConfidence) • (2) Bob must refute C' = C minimally strengthened along quality dimension (using the configuration file constant minStrengthen) with Alice as defender (if not, Bob loses ClaimConfidence). • Then Alice must do the same: Open House 2011

9. Agreement • (1) Alice must defend C against Bob (if not, Alice loses ClaimConfidence) • (2) Alice must refute C' with Bob as defender (if not, Alice loses ClaimConfidence) • If all those protocols produce the result as described, the claim goes into the social welfare set (the knowledge base of claims believed to hold and having maximum strength). Open House 2011

10. Domain • Instance (language) • Solution (language) • boolean valid(Instance) • [0,1] quality(Instance) • InstanceSet (language, subset of Instance) • boolean valid() • boolean belongsTo(Instance) • Response = Instance union Solution Open House 2011

11. SCG(Domain) • Protocol (fixed language) • Claim(Domain) • boolean strengthen(Claim other) // other strengthens this • Domain.InstanceSet getInstanceSet() • Protocol getProtocol() • [0,1] getQuality() • [-1..1] getResult(List(Domain.Response)) Open House 2011

12. Refutations of Claim and !Claim are efficient Claim: F unsatisfiable !Claim: F satisfiable if refuted: Alice does not find satisfying J; baby step towards proof of Claim. If defended: proof of !Claim. Proof: short • if refuted: Bob finds satisfying J; proof of !Claim. • If defended: baby step towards proof of Claim. • Proof: long Roles: Alice claims Bob attempts to refute Open House 2011

13. Both refutations are efficient Claim: Exists F in IS All J: fsat(F,J)<=t !Claim: F has J: fsat(F,J)>=t All F in IS Exists J: fsat(F,J)>=t if refuted: Alice does not find J; baby step towards proof of Claim. If defended: proof of !Claim if Bob is perfect. Proof short. • if refuted: Bob finds J; proof of !Claim assuming Alice is perfect. • If defended: baby step towards proof of Claim. • Proof short. Open House 2011

14. 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 q and using resources at most r. Bionetics 2010

15. Our vision • Researchers and Professors come to the SCG website and configure a new playground X in which tournaments will take place. • Participating teams get baby avatars generated for X that participate in daily competitions. • Competition generates a wealth of information: educated employees/students, good (undefeated) software, good algorithms, good potential employees. Reward is given to the winner. Open House 2011

16. Conclusions • Computational Modeling of Scientific Communities is a good idea: • foster Innovation • improve education • STEM domains: use the web effectively • Current use: • Algorithms class • Software development class Open House 2011

17. Thank you! Open House 2011

18. Strengthening • When claim C is strengthened by Bob to C', Alice must try to refute C' and the strengthening holds only if Bob defends C'. strengthenP(C,C') must hold. • When scholar Bob successfully strengthens a claim of Alice, Bob wins reputation: • Bob + ClaimConfidence + |quality(C)-quality(C')| • When scholar Alice successfully defends her own claim against Bob, Alice wins reputation. • Alice + ClaimConfidence Open House 2011

19. Agreement • When Bob agrees on claim C with Alice, • (1) Bob must defend C against Alice (if not, Bob loses) • (2) Bob must refute C' = C minimally strengthened along quality dimension (using the configuration file constant minStrengthen) with Alice as defender (if not, Bob loses). • Then Alice must do the same: Open House 2011

20. Agreement • (1) Alice must defend C against Bob (if not, Alice loses) • (2) Alice must refute C' with Bob as defender (if not, Alice loses) • If all those protocols produce the result as described, the claim goes into the social welfare set (the knowledge base of claims believed to hold and having maximum strength). Open House 2011

21. Refutations of Claim and !Claim are efficient Claim: F unsatisfiable !Claim: F satisfiable if refuted: Alice does not find satisfying J; baby step towards proof of Claim. If defended: proof of !Claim. Proof: short Alice should never have made the claim! • if refuted: Bob finds satisfying J; proof of !Claim. • If defended: baby step towards proof of Claim. • Proof: long Open House 2011

22. Both refutations are efficient Claim: Exists F in IS All J: fsat(F,J)<=t !Claim: F has J: fsat(F,J)>=t All F in IS Exists J: fsat(F,J)>=t if refuted: Alice does not find J; baby step towards proof of Claim. If defended: proof of !Claim if Bob is perfect. Proof short. Alice should never have made the claim!? • if refuted: Bob finds J; proof of !Claim assuming Alice is perfect. • If defended: baby step towards proof of Claim. • Proof short. Open House 2011

23. Designers • SCG • Domain • includes designing basic components for avatar like standard solvers. Example: HSR: linear search solver • Protocol • Playground: Goal: make playground designers configurators. • Avatar designers Open House 2011

24. Example Playground DesignHighest Safe Rung • Configuration: • domain HSR • claim 1: instanceSetClass protocolClass • claim 2: instanceSetClass !protocolClass • initialReputation = 100 • … Open House 2011

25. Designers: what they produce • SCG /scg • scg.cd, scg.beh • /protocol • Java classes: Singleton Pattern • Domain /domain • /hsr: hsr.cd, hsr.beh • /avatar (components for avatar) • Playground • config file: location of configuration file is given as argument to admin Open House 2011

26. Config • Config = // to configure admin <scgCfg> SCGConfig <domainConfigWrapper> Wrap(DomainConfigI). • Example entries: • domain CSP • claim 1: instanceSetClassprotocolClass • claim 2: instanceSetClass !protocolClass • initialReputation = 100 • … Open House 2011

27. Where can we find configuration settings • If there is a configuration file location given to the admin • in the configuration file • If not: the default value given in the code. Open House 2011

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29. Designers • SCG • Domain • Instance, Solution, InstanceSet, valid, quality • basic domain functionality, like • standard solvers and solvers for niches. • providing instances with “interesting” solutions • Protocol: using protocol language • standard protocols: ForAllExists, PositiveSecret, etc. • Playground: Configurate • Research/Development Managers (Innovation) • Professors (Teaching) • Avatar • researchers, developers • students Open House 2011

30. Example Playground DesignHighest Safe Rung • Configuration: • domain HSR • claim 1: instanceSetClass protocolClass • claim 2: instanceSetClass !protocolClass • initialReputation = 100 • … Open House 2011