By Magnús M. Halldórsson, Kazuo Iwama, Naoki Kobayashi, Bettina Speckmann
The two-volume set LNCS 9134 and LNCS 9135 constitutes the refereed lawsuits of the forty second overseas Colloquium on Automata, Languages and Programming, ICALP 2015, held in Kyoto, Japan, in July 2015. The 143 revised complete papers offered have been rigorously reviewed and chosen from 507 submissions. The papers are equipped within the following 3 tracks: algorithms, complexity, and video games; good judgment, semantics, automata, and conception of programming; and foundations of networked computation: versions, algorithms, and knowledge management.
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Extra info for Automata, Languages, and Programming: 42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 6-10, 2015, Proceedings, Part I
Il Abstract. A randomized encoding of a function f (x) is a randomized function fˆ(x, r), such that the “encoding” fˆ(x, r) reveals f (x) and essentially no additional information about x. Randomized encodings of functions have found many applications in diﬀerent areas of cryptography, including secure multiparty computation, eﬃcient parallel cryptography, and veriﬁable computation. We initiate a complexity-theoretic study of the class SRE of languages (or boolean functions) that admit an eﬃcient statistical randomized encoding.
Un in the input 3 To be precise, we must acknowledge the prior distribution on x which also provides information about its whereabouts. 22 N. Ailon space that is bad in the following sense. For each j ∈ [n ], redeﬁne gj = uTj x to be the input component in direction uj . Again, the variables g1 , . . , gn are iid N (0, Θ(1)). The ﬁrst element in the series, u1 , can be analyzed as xunder (from the previous section) whereby it was argued that before the t1 ’th step, the component g1 = uT1 x can only be known to within an interval of width Ω(γ1 ε), independently of information from components orthogonal to u1 .
For the sake of simplicity the reader is encouraged to assume that F is the Walsh-Hadamard transform, and that by the acronym “FFT” we refer to the fast Walsh-Hadamard transform. The modiﬁcations required for the DFT (rather, the real embedding thereof) require a slight modiﬁcation to the potential function which we mention but do not elaborate on for simplicity. Our results nevertheless apply also to DFT. It is not known whether Ω(n log n) operations are necessary, and this problem is one of the most important open problems in theoretical computer science .