Download Automata, Languages, and Programming: 39th International by Dimitris Achlioptas, Ricardo Menchaca-Mendez (auth.), Artur PDF

By Dimitris Achlioptas, Ricardo Menchaca-Mendez (auth.), Artur Czumaj, Kurt Mehlhorn, Andrew Pitts, Roger Wattenhofer (eds.)

This two-volume set of LNCS 7391 and LNCS 7392 constitutes the refereed court cases of the thirty ninth foreign Colloquium on Automata, Languages and Programming, ICALP 2012, held in Warwick, united kingdom, in July 2012. the entire of 123 revised complete papers provided during this quantity have been conscientiously reviewed and chosen from 432 submissions. they're equipped in 3 tracks focussing on algorithms, complexity and video games; good judgment, semantics, automata and idea of programming; and foundations of networked computation.

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The first case is when m and |S0 | − |S1 | are coprime. The proof makes The NOF Multiparty Communication Complexity of Composed Functions 21 use of the characterization of the MODm function in terms of exponential sums. Fix 2 ≤ m ∈ N and 0 ≤ a, b ≤ m − 1. Let ω = e2πi/m be an m-th root of unity. The function a,b a,b a((∑nj=1 y j )−b) EXP m is defined as EXP m (y1 , y2 , . . , yn ) = ω . The strategy is as follows. Define fm (y1 , . . , yn ) = ∑ j y j mod m. First we show that for any cylinder intersection, the fraction of points x in the cylinder intersection that satisfy fm ◦ g(x) = b is roughly (with exponentially small error) 1/m for all b ∈ {0, 1, .

In: Proceedings of the 24th Annual IEEE Conference on Computational Complexity (CCC), pp. 254–262 (2009) 15. : Disjointness is hard in the multiparty number-on-the-forehead model. Computational Complexity 18, 309–336 (2009) 16. : Composition Theorems in Communication Complexity. G. ) ICALP 2010. LNCS, vol. 6198, pp. 475–489. Springer, Heidelberg (2010) 17. : Personal communication (2006) 18. : The BNS-Chung criterion for multi-party communication complexity. Computational Complexity 9(2), 113–122 (2000) 19.

The protocol proceeds in two steps. In the first step, the players determine the column − g. positions of some u ∈ Hk . Later, they use this to compute the output of f ◦ → ≥3 We now describe the first step. Let X denote the (k − 2) × n dimensional submatrix of X where the first two rows are deleted. Since X ≥3 has n columns and there are 2k−2 possible strings of length k − 2, the string s ∈ {0, 1}k−2 that appears the least number of times as a column of X ≥3 appears at most n/2k−2 times. Without any communication, players 1 and 2 can agree on this string (breaking ties in say lexicographical order).

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