midterm fall 2009 cs 4500

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Midterm Fall 2009 CS 4500 Karl Lieberherr

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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 -> TBall - PowerPoint PPT Presentation

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Page 1: Midterm Fall 2009 CS 4500

Midterm Fall 2009CS 4500

Karl Lieberherr

Page 2: Midterm Fall 2009 CS 4500

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 iff TBallAccept(T(c)) is

winning– T is fast (polynomial time)

Page 3: Midterm Fall 2009 CS 4500

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)

Page 4: Midterm Fall 2009 CS 4500

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 iff FPSAccept(T(c)) is

winning– T is fast (polynomial time)

Page 5: Midterm Fall 2009 CS 4500

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’)

Page 6: Midterm Fall 2009 CS 4500

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))

Page 7: Midterm Fall 2009 CS 4500

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.

Page 8: Midterm Fall 2009 CS 4500

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