References in raw/Page_41.html

• On more dependable assertion-based verification
  C Radojicic, J Moreno, X Pan... - IECON 2013-39th Annual ..., 2013 - ieeexplore.ieee.org
  ... To do so, this section introduces the language of Affine Arithmetic Assertions whose syntax will be described in detail. In order to give a more clear overview of available operators they ...
  

• Spelunking the deep: Guaranteed queries for general neural implicit surfaces
  N Sharp, A Jacobson - arXiv preprint arXiv:2202.02444, 2022 - arxiv.org
  ... functions, and furthermore explicitly defines all affine arithmetic rules used in this work. ... We have now identified variants of affine arithmetic which are wellsuited to computing range ...
  

• Interval Frazer-Duncan criterion for stability analysis of linear systems with dependent coefficients in the characteristic polynomial
  L Kolev, S Petrakieva - Conf. on Circuits - mat.univie.ac.at
  ... Then we apply the necessary simple mathematical operations of modified affine arithmetic (described in previous Section 3) to make a linearization of the resulting functions )( pf . Thus, ...
  

• Using Arithmetic Transform to Calculate Ranges of Arithmetic Datapaths.
  Y Pang, Y Yan, J Wang, Z He, T Liu - J. Comput., 2012 - researchgate.net
  ... The affine arithmetic model (AA) is a derivation of IA borrowed from numerical analysis. In ... [5] take advantage of affine arithmetic modeling to analyze range and precision. Work in [6] ...
  

• Robustness validation of integrated circuits and systems
  M Barke, M Kaergel, W Lu, F Salfelder... - 2012 4th Asia ..., 2012 - ieeexplore.ieee.org
  ... These include the robustness evaluation of digital circuits under aging effects, such as NBTI; the robustness modeling of analog and mixed signal circuits using affine arithmetic; and the ...
  

• Analog Circuit Abstraction to SystemC-AMS Secured by Affine Forms
  A Tarraf, L Hedrich - ... on SMACD and 16th Conference on ..., 2021 - ieeexplore.ieee.org
  ... With the extension of affine arithmetic decision diagrams (AADDs) to SystemC-AMS [2], a system can be described using affine forms to enclose analog behaviors. This allows for the ...
  

• A hybrid algorithm based optimal placement of DG units for loss reduction in the distribution system
  MCV Suresh, JB Edward - Applied Soft Computing, 2020 - Elsevier
  ... To follow the harmonic contributions of individual DGs in conveyance frameworks, A Complex Affine Arithmetic Based Three-Phase Harmonic Power Flow technique (CATHPF) was ...
  

• On a class of parameterized solutions to interval parametric linear systems
  ED Popova - arXiv preprint arXiv:1906.00613, 2019 - arxiv.org
  ... ] is based on affine arithmetic, in Section 3 of this work we propose a parameterized solution in form (2) which is based on the numerical method in [9] and not using affine arithmetic. We ...
  

• Application of Montgomery's trick to scalar multiplication for elliptic and hyperelliptic curves using a fixed base point
  PK Mishra, P Sarkar - International Workshop on Public Key Cryptography, 2004 - Springer
  ... hyperelliptic curve cryptosystems, which uses affine arithmetic and is resistant against simple ... We will refer to these formulae as affine arithmetic. The formulae proposed in [13] do not ...
  

• Fast and effective robustness certification
  G Singh, T Gehr, M Mirman... - Advances in neural ..., 2018 - proceedings.neurips.cc
  ... Since affine arithmetic is fast and exact for affine transformations, it is an attractive candidate for the verification of neural networks [10]. However, the Zonotope abstraction is inherently ...