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ISAAC: A Convolutional Neural Network Accelerator with In-Situ Analog Arithmetic in Crossbars
International Symposium on Computer Architecture, 2016A number of recent efforts have attempted to design accelerators for popular machine learning algorithms, such as those involving convolutional and deep neural networks (CNNs and DNNs).
Ali Shafiee +7 more
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Approximate Arithmetic Circuits: A Survey, Characterization, and Recent Applications
Proceedings of the IEEE, 2020Approximate computing has emerged as a new paradigm for high-performance and energy-efficient design of circuits and systems. For the many approximate arithmetic circuits proposed, it has become critical to understand a design or approximation technique ...
Honglan Jiang +4 more
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Computer arithmetic algorithms
, 2018An explanation of the principles of the algorithms available for performing arithmetic operations in digital computers. The algorithms are described independently of specific implementation technology and within the same framework, so that similarities ...
I. Koren
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Mathematical Logic Quarterly, 1998
AbstractWe develop arithmetical measure theory along the lines of Lutz [10]. This yields the same notion of measure 0 set as considered before by Martin‐Löf, Schnorr, and others. We prove that the class of sets constructible by r.e.‐constructors, a direct analogue of the classes Lutz devised his resource bounded measures for in [10], is not equal to RE,
Terwijn, S., Torenvliet, L.
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AbstractWe develop arithmetical measure theory along the lines of Lutz [10]. This yields the same notion of measure 0 set as considered before by Martin‐Löf, Schnorr, and others. We prove that the class of sets constructible by r.e.‐constructors, a direct analogue of the classes Lutz devised his resource bounded measures for in [10], is not equal to RE,
Terwijn, S., Torenvliet, L.
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Arithmetic in Peano Arithmetic
2020In this chapter, we take a closer look at Peano Arithmetic (PA) which we have defined in Chapter 1. In particular, we prove within PA some basic arithmetical results, starting with the commutativity and associativity of addition and multiplication, culminating in some results about coprimality.
Lorenz Halbeisen, Regula Krapf
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Journal of the London Mathematical Society, 1991
The group \(\hbox{Sym }\mathbb{R}\) of permutations of the set \(\mathbb{R}\) of real numbers is considered in the paper. Let \(P_ 0\) be its subgroup of power functions \(x\mapsto x^{m/n}\) where \(m\), \(n\) are positive odd integers, \(T\) be the subgroup of translations \(x\mapsto x+a\) where \(a\) is a real algebraic number, and \(M\) be the ...
Adeleke, S. A. +2 more
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The group \(\hbox{Sym }\mathbb{R}\) of permutations of the set \(\mathbb{R}\) of real numbers is considered in the paper. Let \(P_ 0\) be its subgroup of power functions \(x\mapsto x^{m/n}\) where \(m\), \(n\) are positive odd integers, \(T\) be the subgroup of translations \(x\mapsto x+a\) where \(a\) is a real algebraic number, and \(M\) be the ...
Adeleke, S. A. +2 more
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Arithmetic is not arithmetic: Paradigm matters for arithmetic effects
CognitionResearch on arithmetic uses different experimental paradigms. So far, it is unclear whether these different paradigms lead to the same effects or comparable effect sizes. Therefore, this study explores how different experimental paradigms influence mental arithmetic performance, focusing on understanding the potential differences and similarities in ...
Xinru, Yao +3 more
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SOLVABLE ARITHMETIC GROUPS AND ARITHMETICITY PROBLEMS
International Journal of Mathematics, 1999We describe solvable arithmetic groups for which natural rigidity properties hold and solve the arithmeticity problem for the automorphism groups of these arithmetic groups and further prove arithmeticity results for their finite extensions. We also solve the arithmeticity problem for polycyclic groups. We prove that there are non-arithmetic polycyclic
Grunewald, Fritz, Platonov, Vladimir
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Finite Precision Rational Arithmetic: An Arithmetic Unit
IEEE Transactions on Computers, 1983The foundations of an arithmetic unit performing the add, subtract, multiply, and divide operations on rational operands are developed. The unit uses the classical Euclidean algorithm as one unified algorithm for all the arithmetic operations, including rounding.
Kornerup, Peter, Matula, David W.
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Additive Arithmetic Functions on Arithmetic Progressions
Proceedings of the London Mathematical Society, 1987For an additive arithmetic function f, and positive integer D, let E(x,D) be \[ \max_{y\leq x}\max_{(r,D)=1}| \sum_{n\leq y,\quad n\equiv r (mod D)}f(n)-(1/\phi (D))\sum_{n\leq y,\quad (n,D)=1}f(n)|. \] Strengthening results from Chapter 7 of his monograph ''Arithmetic functions and integer products'' (1985; Zbl 0559.10032), the author proves that for ...
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