Midterm Fall 2009 CS 4500

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# Midterm Fall 2009 CS 4500 - PowerPoint PPT Presentation

Midterm Fall 2009 CS 4500. Karl Lieberherr. 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 -&gt; TBall

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### Midterm Fall 2009CS 4500

Karl Lieberherr

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)
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)
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)
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’)
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))
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.
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