532 research outputs found
Logic synthesis and testing techniques for switching nano-crossbar arrays
Beyond CMOS, new technologies are emerging to extend electronic systems with features unavailable to silicon-based devices. Emerging technologies provide new logic and interconnection structures for computation, storage and communication that may require new design paradigms, and therefore trigger the development of a new generation of design automation tools. In the last decade, several emerging technologies have been proposed and the time has come for studying new ad-hoc techniques and tools for logic synthesis, physical design and testing. The main goal of this project is developing a complete synthesis and optimization methodology for switching nano-crossbar arrays that leads to the design and construction of an emerging nanocomputer. New models for diode, FET, and four-terminal switch based nanoarrays are developed. The proposed methodology implements logic, arithmetic, and memory elements by considering performance parameters such as area, delay, power dissipation, and reliability. With combination of logic, arithmetic, and memory elements a synchronous state machine (SSM), representation of a computer, is realized. The proposed methodology targets variety of emerging technologies including nanowire/nanotube crossbar arrays, magnetic switch-based structures, and crossbar memories. The results of this project will be a foundation of nano-crossbar based circuit design techniques and greatly contribute to the construction of emerging computers beyond CMOS. The topic of this project can be considered under the research area of â\u80\u9cEmerging Computing Modelsâ\u80\u9d or â\u80\u9cComputational Nanoelectronicsâ\u80\u9d, more specifically the design, modeling, and simulation of new nanoscale switches beyond CMOS
Limitations of semidefinite programs for separable states and entangled games
Semidefinite programs (SDPs) are a framework for exact or approximate
optimization that have widespread application in quantum information theory. We
introduce a new method for using reductions to construct integrality gaps for
SDPs. These are based on new limitations on the sum-of-squares (SoS) hierarchy
in approximating two particularly important sets in quantum information theory,
where previously no -round integrality gaps were known: the set of
separable (i.e. unentangled) states, or equivalently, the
norm of a matrix, and the set of quantum correlations; i.e. conditional
probability distributions achievable with local measurements on a shared
entangled state. In both cases no-go theorems were previously known based on
computational assumptions such as the Exponential Time Hypothesis (ETH) which
asserts that 3-SAT requires exponential time to solve. Our unconditional
results achieve the same parameters as all of these previous results (for
separable states) or as some of the previous results (for quantum
correlations). In some cases we can make use of the framework of
Lee-Raghavendra-Steurer (LRS) to establish integrality gaps for any SDP, not
only the SoS hierarchy. Our hardness result on separable states also yields a
dimension lower bound of approximate disentanglers, answering a question of
Watrous and Aaronson et al. These results can be viewed as limitations on the
monogamy principle, the PPT test, the ability of Tsirelson-type bounds to
restrict quantum correlations, as well as the SDP hierarchies of
Doherty-Parrilo-Spedalieri, Navascues-Pironio-Acin and Berta-Fawzi-Scholz.Comment: 47 pages. v2. small changes, fixes and clarifications. published
versio
A Study of Sparse Representation of Boolean Functions
Boolean function is one of the most fundamental computation models in theoretical computer science. The two most common representations of Boolean functions are Fourier transform and real polynomial form. Applying analytic tools under these representations to the study Boolean functions has led to fruitful research in many areas such as complexity theory, learning theory, inapproximability, pseudorandomness, metric embedding, property testing, threshold phenomena, social choice, etc. In this thesis, we focus on \emph{sparse representations} of Boolean function in both Fourier transform and polynomial form, and obtain the following new results. A classical result of Rothschild and van Lint asserts that if every non-zero Fourier coefficient of a Boolean function over has the same absolute value, namely for every in the Fourier support of , then must be the indicator function of some affine subspace of dimension . Here we slightly generalize their result, and show that Boolean functions whose Fourier coefficients take values in the set are indicator functions of two disjoint affine subspaces of dimension or four disjoint affine subspaces of dimension . Our main technical tools are results from additive combinatorics which offer tight bounds on the affine span size of a subset of when the doubling constant of the subset is small. For polynomial representation of Boolean function, we study the distribution of the number of non-zero coefficients of \emph{random} Boolean functions. For a random Boolean function , i.e., a function whose value at each point on the Boolean cube is chosen independently and uniformly at random from , in real polynomial representation, we give several bounds and concentration results about the distribution of the sparsity of
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