midterm fall 2009 cs 4500 karl lieberherr. black box for tball want to use it to play slow pitch...
DESCRIPTION
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)TRANSCRIPT
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Midterm Fall 2009CS 4500
Karl Lieberherr
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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 Karl Lieberherr. Black box for TBall Want to use it to play Slow Pitch Softball.…](https://reader036.vdocuments.mx/reader036/viewer/2022090107/5a4d1be17f8b9ab0599dfec6/html5/thumbnails/3.jpg)
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 Karl Lieberherr. Black box for TBall Want to use it to play Slow Pitch Softball.…](https://reader036.vdocuments.mx/reader036/viewer/2022090107/5a4d1be17f8b9ab0599dfec6/html5/thumbnails/4.jpg)
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 Karl Lieberherr. Black box for TBall Want to use it to play Slow Pitch Softball.…](https://reader036.vdocuments.mx/reader036/viewer/2022090107/5a4d1be17f8b9ab0599dfec6/html5/thumbnails/5.jpg)
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’)
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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))
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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.
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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