1 / 8

Midterm Fall 2009 CS 4500

This text discusses the use of black boxes for translating between different softball games and graph theory problems. It explores the reduction of Slow Pitch Softball to TBall and Midterm Softball to Fast Pitch Softball. Additionally, it covers challenges in translating between 3-SAT and 3-Coloring problems using black boxes. The text also presents scenarios where players test translations and demonstrate their understanding through challenges and code reviews.

ullrich
Download Presentation

Midterm Fall 2009 CS 4500

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Midterm Fall 2009CS 4500 Karl Lieberherr

  2. Black box for TBall • Want to use it to play Slow Pitch Softball. • Slow Pitch Softball is reducible to TBall. • The black box contains: • TBallOffer, TBallAccept, TBallProvide, TBallSolve • Translation T: SPS -> TBall • Accept(SPS c) is winning iffTBallAccept(T(c)) is winning • T is fast (polynomial time)

  3. Similar situation from Theory of Computation • Black box for 3-Coloring a graph. • We want to use it to solve the 3-SAT problem. • The black box contains: HasA-3Coloring(graph g) • Translation T: 3-SAT -> 3-Coloring • s is satisfiable iff T(s) has a 3-Coloring • T is fast (polynomial time)

  4. Black box for Fast Pitch Softball (FPS) • Want to use it to play Midterm Softball (MS). • The black box contains: • TBallOffer, TBallAccept, TBallProvide, TBallSolve • Translation T: MS-> FPS • Accept(MS c) is winning iffFPSAccept(T(c)) is winning • T is fast (polynomial time)

  5. ST: Slow Pitch Softball (SPS) is reducible to TBall • Offer • Use TBallOffer to create TBall challenge. Add some implied relations. • Accept(SPS c) • TBallAccept(ST(c)) • Provide(SPS c) • TBallProvide(ST(c)) • Solve(SPS c, Problem p) • p’=Filter ST(c) constraints in p; TBallSolve(ST(c), p’)

  6. MF: Midterm Softball (MS) is reducible to Fast Pitch Softball (FPS) MFC: Translate Midterm challenge to (R1,R2) Fast Pitch Softball challenge. MFP: MS problems -> FPS problems FMP: FPS_MS problems -> MS problems • Offer • Create MS challenge mch; Use FPSBreakEven(MFC(mch)) to compute price • Accept(MS c) • FPSAccept(MFC(c)) • Provide(MS c) • FMP(FPSProvide(MFC(c))) • Solve(MS c, Problem p) • FPSSolve(MFC(c), MFP(p))

  7. Playing SCG-Scholar for MS->FPS • Alice claims: I understand MS->FPS • Bob opposes Alice. • Bob gives her a winning MS challenge • Alice translates it to FPS • The FPS challenge is not winning. Alice loses; she has demonstrated that she does not understand MS->FPS.

  8. Playing SCG-Scholar for MS->FPS:Another variant: code review • Alice claims: I have a correct translation T:MS-FPS. • Bob opposes Alice. • Alice gives her code for T to Bob. • Bob does a code review of T and finds an input where T fails. • Bob wins: he has demonstrated to Alice that she does not have a correct translation

More Related