The Algorithms we use to learn about Algorithms Karl Lieberherr Ahmed Abdelmeged 3/16/20111Open House 2011

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 3/16/20112Open House 2011

Idea: Use Scientific Community Model to 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. 3/16/20113Open House 2011

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 3/16/20114Open House 2011

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) 3/16/2011Open House 20115

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 3/16/2011Open House 20116

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 3/16/2011Open House 20117

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: 3/16/2011Open House 20118

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). 3/16/2011Open House 20119

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 3/16/201110Open House 2011

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)) 3/16/201111Open House 2011

Refutations of Claim and !Claim are efficient Claim: F unsatisfiable if refuted: Bob finds satisfying J; proof of !Claim. If defended: baby step towards proof of Claim. Proof: long !Claim: F satisfiable if refuted: Alice does not find satisfying J; baby step towards proof of Claim. If defended: proof of !Claim. Proof: short 3/16/201112Open House 2011 Roles: Alice claims Bob attempts to refute

Both refutations are efficient Claim: Exists F in IS All J: fsat(F,J)<=t if refuted: Bob finds J; proof of !Claim assuming Alice is perfect. If defended: baby step towards proof of Claim. Proof short. !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. 3/16/201113Open House 2011

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. 14Bionetics 2010

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. 3/16/2011Open House

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 3/16/2011Open House

Thank you! 3/16/2011Open House

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 3/16/2011Open House

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: 3/16/2011Open House

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). 3/16/2011Open House

Refutations of Claim and !Claim are efficient Claim: F unsatisfiable if refuted: Bob finds satisfying J; proof of !Claim. If defended: baby step towards proof of Claim. Proof: long !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! 3/16/201121Open House 2011

Both refutations are efficient Claim: Exists F in IS All J: fsat(F,J)<=t if refuted: Bob finds J; proof of !Claim assuming Alice is perfect. If defended: baby step towards proof of Claim. Proof short. !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!? 3/16/201122Open House 2011

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 3/16/201123Open House 2011

Example Playground Design Highest Safe Rung Configuration: – domain HSR – claim 1: instanceSetClass protocolClass – claim 2: instanceSetClass !protocolClass – initialReputation = 100 – … 3/16/201124Open House 2011

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 3/16/201125Open House 2011

Config Config = // to configure admin SCGConfig Wrap(DomainConfigI). Example entries: – domain CSP – claim 1: instanceSetClass protocolClass – claim 2: instanceSetClass !protocolClass – initialReputation = 100 – … 3/16/201126Open House 2011

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. 3/16/201127Open House 2011

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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 3/16/201129Open House 2011

Example Playground Design Highest Safe Rung Configuration: – domain HSR – claim 1: instanceSetClass protocolClass – claim 2: instanceSetClass !protocolClass – initialReputation = 100 – … 3/16/201130Open House 2011