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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

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black box for tball
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
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
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
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
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
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
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
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