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The approximate degree of a Boolean function f: {-1, 1}^n ↦ {-1, 1} is the least degree of a real polynomial that approximates f pointwise to error at most 1/3. We introduce a generic method for increasing the approximate degree of a given function, while preserving its computability by constant-depth circuits.Specifically, we show how to transform any Boolean function f with approximate...
For odd integers p ≥ 1 (and p = ∞), we show that the Closest Vector Problem in the ℓp norm (CVP_p) over rank n lattices cannot be solved in 2^(1-≥) n time for any constant ≥ 0 unless the Strong Exponential Time Hypothesis (SETH) fails. We then extend this result to almost all values of p ≥ 1, not including the even integers. This comes...
The random k-SAT model is the most important and well-studied distribution over k-SAT instances. It is closely connected to statistical physics and is a benchmark for satisfiability algorithms. We show that when k = Θ(log n), any Cutting Planes refutation for random k-SAT requires exponential size in the interesting regime where the number of clauses guarantees that the formula is unsatisfiable...
We show that if the nearly-linear time solvers for Laplacian matrices and their generalizations can be extended to solve just slightly larger families of linear systems, then they can be used to quickly solve all systems of linear equations over the reals. This result can be viewed either positively or negatively: either we will develop nearly-linear time algorithms for solving all systems of linear...
We consider the fundamental derandomization problem of deterministically finding a satisfying assignment to a CNF formula that has many satisfying assignments. We give a deterministic algorithm which, given an n-variable \poly(n)-clause CNF formula F that has at least ≥ 2^n satisfying assignments, runs in time \[ n^{\tilde{O}(\log\log n)^2} \] for ≥ \ge 1/\polylog(n) and outputs...
We develop several efficient algorithms for the classical Matrix Scaling} problem, which is used in many diverse areas, from preconditioning linear systems to approximation of the permanent. On an input n× n matrix A, this problem asks to find diagonal (scaling) matrices X and Y (if they exist), so that X A Y ε-approximates a doubly stochastic matrix, or more generally a matrix...
Companies of the engineer-to-order (ETO) business face various trends such as digitalization and globalization. These trends will radically impact our ways of engineering. The Engineering framework translates Dave Snowden's Cynefin framework [2] to the engineering world. Cynefin for Engineers allows structuring future ways of engineering and guiding ETO companies along their transformation of engineering...
We present a new distributed} model of probabilistically checkable proofs (PCP). A satisfying assignment x ∊ \{0,1\}^n to a CNF formula \phi is shared between two parties, where Alice knows x_1, \dots, x_{n/2, Bob knows x_{n/2+1},\dots,x_n, and both parties know \phi. The goal is to have Alice and Bob jointly write a PCP that x satisfies \phi, while exchanging little or no information....
We consider properties of edge-colored vertex-ordered graphs} – graphs with a totally ordered vertex set and a finite set of possible edge colors – showing that any hereditary property of such graphs is strongly testable, i.e., testable with a constant number of queries. We also explain how the proof can be adapted to show that any hereditary property of two-dimensional matrices...
Several cases are known where faults in spreadsheets have caused severe losses of money for companies. Besides other factors, the non-existence of advanced testing and debugging mechanisms in environments like MS Excel causes faults in spreadsheets to remain undetected. In this paper we describe the main functionality of the EXQUISITE tool, a software system and add-in to MS Excel that was developed...
End-user programming in smart homes addresses tasks that range from very simple to very complex. In this study we investigate how task complexity impacts performance when using two different visual programing representations: form-filling and data-flow programming. We invited 16 participants to create rules to solve smart-home situations of varying complexity and analyzed their completion rates for...
Based on a literature analysis, this paper examines the nature of evolution in Systems of Systems (SoS) by attempting to answer why, where and how change occurs in this new kind of complex systems as well as what unprecedented underlying challenges makes it difficult to manage. This paper gives special focus on how state-of-the-art research efforts are attempting to solve those challenges and ultimately...
In this paper, the principle of normalized minimum-sum (NMS) polar decoding process is explored. It is demonstrated that with one properly chosen parameters for NMS algorithm, performances approach to that of the sum-product (SP) algorithm can be achieved. As well, the complexity reduction is realized by calculating a linear function instead of nonlinear function. Simulation results for successive...
High Efficiency Video Coding (Hevc), the newest video encoding standard, provides up to 50% bitrate savings compared to the state-of-art H.264/AVC standard for the same perceptual video quality. In the last few years, the Internet of Things (IoT) has become a reality. Forthcoming applications are likely to boost mobile video demand to an unprecedented level. A large number of systems are likely to...
Orthogonal Frequency Division Multiplexing (OFDM) is a technique, which is widely used in 4G and considered in 5G wireless communication system these days. It is a form of multi-carrier modulation technique. One major disadvantage of OFDM is that the time domain OFDM signal leads to a high peak-to-average power ratio (PAPR). In this paper we propose a new selective tone reservation (STR) algorithm...
Universal Filtered Orthogonal Frequency Division Multiplexing (UF-OFDM) is considered one of the main wave-form candidates to overcome the challenges facing the next generation of mobile communication systems. Due to its spectral properties it can support relaxed synchronization, low-latency communications and flexible time transmission interval. Nevertheless, the available recent literature addresses...
This paper proposes a low complex hardware accelerator algorithmic modification for n-dimensional (nD) FastICA methodology based on Coordinate Rotation Digital Computer (CORDIC) to attain high computation speed. The most complex and time consuming update stage and convergence check required for computation of the nth weight vector are eliminated in the proposed methodology. Using the Gram-Schmidt...
Deep learning recently shows strong competitiveness to improve polar code decoding. However, suffering from prohibitive training and computation complexity, the conventional deep neural network (DNN) is only possible for very short code length. In this paper, the main problems of deep learning in decoding are well solved. We first present the multiple scaled belief propagation (BP) algorithm, aiming...
The U.S. Department of Energy (DOE) Office of Science (SC) operates approximately four dozen large-scale science user facilities (SUFs), each of which generates a tremendous amount of scientific data from experiments, observations and computations. To better understand the data needs and challenges, DOE has run many workshops in recent years to identify and articulate data-centric challenges and opportunities...
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