By Manuel Blum (auth.), My T. Thai, Sartaj Sahni (eds.)
This ebook constitutes the court cases of the sixteenth Annual overseas convention on Computing and Combinatorics, held in Nha Trang, Vietnam, in July 2010.
Read Online or Download Computing and Combinatorics: 16th Annual International Conference, COCOON 2010, Nha Trang, Vietnam, July 19-21, 2010. Proceedings PDF
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Extra info for Computing and Combinatorics: 16th Annual International Conference, COCOON 2010, Nha Trang, Vietnam, July 19-21, 2010. Proceedings
R R For k provers, a function pi is no-signaling if: ∀x ∈ Xi , a ∈ Ai , xj , xj ∈ Xj for j=i Pr[pi (x1 , . . xi−1 , x, xi+1 , . . xk , R) = a] = R Pr[pi (x1 , . . xi−1 , x, xi+1 , . . xk , R) = a]. 1 (value of the Game). The value of the game is defined as: ω ♦ (G)= max EXY ZR [Q(X, Y, Z, p1 (X, Y, Z, R), p2 (X, Y, Z, R), p3 (X, Y, Z, R))] p1 ,p2 ,p3 where the expectation is taken with respect to PXY Z and the maximum is taken over all No-Signaling protocols. The n-fold parallel repetition 3-provers game G⊗n consists of the sets X n , Y n , Z n , ⊗n a probability measure on those sets, PX n Y n Z n where ⊗n n n n PX n Y n Z n (x , y , z ) n PXY Z (xi , yi , zi ) = i=1 for xn ∈ X n , y n ∈ Y n , z n ∈ Z n .
LNCS, vol. 5555, pp. 71–82. Springer, Heidelberg (2009) 4. : Constant time generation of rooted trees. SIAM Journal on Computing 9(4), 706–712 (1980) 5. : On problems without polynomial kernels (extended abstract). , Walukiewicz, I. ) ICALP 2008, Part I. LNCS, vol. 5125, pp. 563–574. Springer, Heidelberg (2008) 6. : Kernel bounds for disjoint cycles and disjoint paths. , Sanders, P. ) ESA 2009. LNCS, vol. 5757, pp. 635–646. Springer, Heidelberg (2009) 7. : Vertex Cover: Further observations and further improvements.
This is a generalization of Lemma 23 in Holenstein’s paper [Hol07]. We then conclude that the provers can not win the game im with probability greater than ω ♦ (G) + . 1 (RazHolenstein). , PU is a product distribution over U1 , . . U ) and let W be some event, then the following holds: PUi |W − PUi ≤ · log i=1 1 Pr[W ] For completeness, we include the proof of the lemma in full version of the paper. 1. 2. Let PT U = PT PU1 |T PU2 |T · · · PU then the following holds: PT Ui |W − PT |W PUi |T ≤ |T and let W be some event, · log i=1 1 Pr[W ] For the proof see full version of the paper.
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