Our central result asserts that a (logical) language preserved under extension of models has a 0-1 law under the uniform probability distribution. We then investigate some fragments of the first-order infinitary logic...
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Our central result asserts that a (logical) language preserved under extension of models has a 0-1 law under the uniform probability distribution. We then investigate some fragments of the first-order infinitary logic L-infinity omega and of second-order logic which are preserved under extension. This paper reveals new boundaries of 0-1 laws for fragments of L-infinity omega and of second-order logic. The latter fragments are particularly interesting as they capture the prototypical complete problem for each level of the polynomial-time hierarchy.
The use of one-bit analog-to-digital converter (ADC) has been considered as a viable alternative to high resolution counterparts in realizing and commercializing massive multiple-input multiple-output (MIMO) systems. ...
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The use of one-bit analog-to-digital converter (ADC) has been considered as a viable alternative to high resolution counterparts in realizing and commercializing massive multiple-input multiple-output (MIMO) systems. However, the issue of discarding the amplitude information by one-bit quantizers has to be compensated. Thus, carefully tailored methods need to be developed for one-bit channel estimation and data detection as the conventional ones cannot be used. To address these issues, the problems of one-bit channel estimation and data detection for MIMO orthogonal frequency division multiplexing (OFDM) system that operates over uncorrelated frequency selective channels are investigated here. We first develop channel estimators that exploit Gaussian discriminant analysis (GDA) classifier and approximate versions of it as the so-called weak classifiers in an adaptive boosting (AdaBoost) approach. Particularly, the combination of the approximate GDA classifiers with AdaBoost offers the benefit of scalability with the linear order of computations, which is critical in massive MIMO-OFDM systems. We then take advantage of the same idea for proposing the data detectors. Numerical results validate the efficiency of the proposed channel estimators and data detectors compared to other methods. They show comparable/better performance to that of the state-of-the-art methods, but require dramatically lower computational complexities and run times.
We consider the computationally efficient direction-of-arrival (DOA) and noncircular (NC) phase estimation problem of noncircular signal for uniform linear array. The key idea is to apply the noncircular propagator me...
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We consider the computationally efficient direction-of-arrival (DOA) and noncircular (NC) phase estimation problem of noncircular signal for uniform linear array. The key idea is to apply the noncircular propagator method (NC-PM) which does not require eigenvalue decomposition (EVD) of the covariance matrix or singular value decomposition (SVD) of the received data. Noncircular rotational invariance propagator method (NC-RI-PM) avoids spectral peak searching in PM and can obtain the closed-form solution of DOA, so it has lower computational complexity. An improved NC-RI-PM algorithm of noncircular signal for uniform linear array is proposed to estimate the elevation angles and noncircular phases with automatic pairing. We reconstruct the extended array output by combining the array output and its conjugated counterpart. Our algorithm fully uses the extended array elements in the improved propagator matrix to estimate the elevation angles and noncircular phases by utilizing the rotational invariance property between subarrays. Compared with NC-RI-PM, the proposed algorithm has better angle estimation performance and much lower computational load. The computational complexity of the proposed algorithm is analyzed. We also derive the variance of estimation error and Cramer-Rao bound (CRB) of noncircular signal for uniform linear array. Finally, simulation results are presented to demonstrate the effectiveness of our algorithm.
Although zero-forcing ( ZF) detection is well-known for its low computational complexity in multiple-input multiple-output ( MIMO) communication systems, it suffers from significantly poor performance. The sphere deco...
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Although zero-forcing ( ZF) detection is well-known for its low computational complexity in multiple-input multiple-output ( MIMO) communication systems, it suffers from significantly poor performance. The sphere decoder ( SD) method, on the other hand, achieves the maximum likelihood ( ML) performance yet imposes a high computational complexity. We propose a low-complexity detection scheme, concatenated with the SD method, which verifies the reliability of the ZF equalized observations via some predefined regions and thresholds obtained by the channel realization. We design the threshold analytically, such that the method achieves the ML performance. With the designed threshold, we prove that the method achieves the ML performance and the ZF computational complexity at the same time with probability one, at high signal-to-noise ratio ( SNR). The theoretical analysis is corroborated with numerical simulations. The simulation results also show that the proposed method achieves the ML performance very rapidly as the SNR increases.
We prove a superlinear lower bound on the size of a bounded depth bilinear arithmetical circuit computing cyclic convolution. Our proof uses the strengthening of the Donoho-Stark uncertainty principle [D.L. Donoho, P....
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We prove a superlinear lower bound on the size of a bounded depth bilinear arithmetical circuit computing cyclic convolution. Our proof uses the strengthening of the Donoho-Stark uncertainty principle [D.L. Donoho, P.B. Stark, Uncertainty principles and signal recovery, SIAM journal of Applied Mathematics 49 (1989) 906-931] given by [Tao IT. Tao, An uncertainty principle for cyclic groups of prime order, Mathematical Research Letters 12 (2005) 121-127], and a combinatorial lemma by Raz and Shpilka [R. Raz, A. Shpilka, Lower bounds for matrix product, in arbitrary circuits with bounded gates, SIAM Journal of Computing 32 (2003) 488-513]. This combination and an observation on ranks of circulant matrices, which we use to give a much shorter proof of the Donoho-Stark principle, may have other applications. (C) 2008 Elsevier B.V. All rights reserved.
To monitor electrical activity throughout the power grid and mitigate outages, sensors known as phasor measurement units can installed. Due to implementation costs, it is desirable to minimize the number of sensors de...
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To monitor electrical activity throughout the power grid and mitigate outages, sensors known as phasor measurement units can installed. Due to implementation costs, it is desirable to minimize the number of sensors deployed while ensuring that the grid can be effectively monitored. This optimization problem motivates the graph theoretic power dominating set problem. In this paper, we propose a method for computing minimum power dominating sets via a set cover IP formulation and a novel constraint generation procedure. The set cover problem's constraints correspond to neighborhoods of zero forcing forts;we study their structural properties and show they can be separated with delayed row generation. In addition, we offer several computation enhancements which be be applied to our methodology as well as existing methods. The proposed and existing methods are evaluated in several computational experiments. In many of the larger test instances considered, the proposed method exhibits an order of magnitude runtime performance improvement.
We prove a number of general theorems about ZK, the class of problems possessing ( computational) zero-knowledge proofs. Our results are unconditional, in contrast to most previous works on ZK, which rely on the assum...
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We prove a number of general theorems about ZK, the class of problems possessing ( computational) zero-knowledge proofs. Our results are unconditional, in contrast to most previous works on ZK, which rely on the assumption that one-way functions exist. We establish several new characterizations of ZK and use these characterizations to prove results such as the following: 1. Honest-verifier ZK equals general ZK. 2. Public-coin ZK equals private-coin ZK. 3. ZK is closed under union. 4. ZK with imperfect completeness equals ZK with perfect completeness. 5. Any problem in ZK boolean AND NP can be proven in computational zero knowledge by a BPPNP prover. 6. ZK with black-box simulators equals ZK with general, non-black-box simulators. The above equalities refer to the resulting class of problems ( and do not necessarily preserve other efficiency measures such as round complexity). Our approach is to combine the conditional techniques previously used in the study of ZK with the unconditional techniques developed in the study of SZK, the class of problems possessing statistical zero-knowledge proofs. To enable this combination, we prove that every problem in ZK can be decomposed into a problem in SZK together with a set of instances from which a one-way function can be constructed.
We provide new non-approximability results for the restrictions of the MIN VERTEX COVER problem to bounded-degree, sparse and dense graphs. We show that for a sufficiently large B, the recent 1.16 lower bound proved b...
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We provide new non-approximability results for the restrictions of the MIN VERTEX COVER problem to bounded-degree, sparse and dense graphs. We show that for a sufficiently large B, the recent 1.16 lower bound proved by Hastad (1997) extends with negligible loss to graphs with bounded degree B. Then, we consider sparse graphs with no dense components (i.e. everywhere sparse graphs), and we show a similar result but with a better trade-off between non-approximability and sparsity, Finally, we observe that the MIN VERTEX COVER problem remains APX-complete when restricted to dense graph and thus recent techniques developed for several MAX SNP problems restricted to "dense" instances introduced by Arora et al. (1995) cannot be applied. (C) 1999 Elsevier Science B.V. All rights reserved.
Ordered Binary Decision Diagrams (OBDDs) are graph-based representations of Boolean functions which are widely used because of their good properties. In this paper, we introduce nondeterministic OBDDs (NOBDDs) and the...
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Ordered Binary Decision Diagrams (OBDDs) are graph-based representations of Boolean functions which are widely used because of their good properties. In this paper, we introduce nondeterministic OBDDs (NOBDDs) and their restricted forms, and evaluate their expressive power. In some applications of OBDDs, canonicity, which is one of the good properties of OBDDs, is not necessary. In such cases, we can reduce the required amount of storage by using OBDDs in some non-canonical form. A class of NOBDDs can be used as a non-canonical form of OBDDs. In this paper, we focus on two particular methods which can be regarded as using restricted forms of NOBDDs. Our aim is to show how the size of OBDDs can be reduced in such forms from theoretical point of view. Firstly, we consider a method to solve satisfiability problem of combinational circuits using the structure of circuits as a key to reduce the NOBDD size. We show that the NOBDD size is related to the cutwidth of circuits. Secondly, we analyze methods that use OBDDs to represent Boolean functions as sets of product terms. We show that the class of functions treated feasibly in this representation strictly contains that in OBDDs and contained by that in NOBDDs.
For delta is an element of (0, 1) and k, n is an element of N, we study the task of transforming a hard function f : {0, 1}(n) -> {0, 1}, with which any small circuit disagrees on (1 - delta)/2 fraction of the inpu...
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For delta is an element of (0, 1) and k, n is an element of N, we study the task of transforming a hard function f : {0, 1}(n) -> {0, 1}, with which any small circuit disagrees on (1 - delta)/2 fraction of the input, into a harder function f', with which any small circuit disagrees on (1 - delta(k))/2 fraction of the input. First, we show that such hardness amplification, when carried out in some black-box way, must require a high complexity. In particular, it cannot be realized by a circuit of depth d and size 2(o(k1/d)) or by a nondeterministic circuit of size o(k/log k) (and arbitrary depth) for any delta is an element of (0, 1). This extends the result of Viola, which only works when (1 - delta)/2 is small enough. Furthermore, we show that even without any restriction on the complexity of the amplification procedure, such a black-box hardness amplification must be inherently nonuniform in the following sense. To guarantee the hardness of the resulting function f', even against uniform machines, one has to start with a function f, which is hard against nonuniform algorithms with Omega(k log(1/delta)) bits of advice. This extends the result of Trevisan and Vadhan, which only addresses the case with (1 - delta)/2 = 2(-n). Finally, we derive similar lower bounds for any black-box construction of a pseudorandom generator (PRG) from a hard function. To prove our results, we link the task of hardness amplifications and PRG constructions, respectively, to some type of error-reduction codes, and then we establish lower bounds for such codes, which we hope could find interest in both coding theory and complexity theory.
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