By Magnús M. Halldórsson, Kazuo Iwama, Naoki Kobayashi, Bettina Speckmann
The two-volume set LNCS 9134 and LNCS 9135 constitutes the refereed complaints 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 conscientiously reviewed and chosen from 507 submissions. The papers are geared up within the following 3 tracks: algorithms, complexity, and video games; common sense, semantics, automata, and conception of programming; and foundations of networked computation: versions, algorithms, and data management.
Read or Download Automata, Languages, and Programming: 42nd International Colloquium, ICALP 2015, Kyoto, Japan, July 6-10, 2015, Proceedings, Part I PDF
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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
Let I denote the set of possible inputs, given the information we are left with upon termination. Consider the projection Q2 onto the space orthogonal to u1 = z1 / z1 , as a function deﬁned over I. Let I2 = Q2 I denote its image. The preimage of any point w ∈ I2 must contain a line segment of length at least εγ1 parallel to u1 , due to the uncertainty in xT u1 . 4 Continuing inductively, we lower bound the (n − j + 1)-volume of Ij := Qj I = Qj Ij−1 for j > 2. Consider the projection Qj as a function operating on Ij−1 , and any point w in the image Ij .
DLWE approximately classiﬁes noisy codewords (A, b = As+e) into Yes and No instances, depending upon on the size of the error vector e. Roughly speaking, Yes instances correspond to small errors and No instances to large errors. Note that, an SRE encoding of input (A, b = As + e) must be oblivious of all information about A, s, e except the relative size of the error vector e. We begin by using the additive homomorphism of the LWE secret to mask s. Speciﬁcally, we choose a random vector t and compute b = b + At = A(s + t) + e.
It is beyond the scope of this work to survey all uses of Fourier transforms in both theory of algorithms and in complexity. 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.