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Asymptotically best method for synthesis of Boolean recursive circuits

  • Vladimir V. Zhukov EMAIL logo and Sergey A. Lozhkin
Published/Copyright: April 29, 2020

Abstract

Models of multi-output and scalar recursive Boolean circuits of bounded depth in an arbitrary basis are considered. Methods for lower and upper estimates for the Shannon function for the complexity of circuits of these classes are provided. Based on these methods, an asymptotic formula for the Shannon function is put forward. Moreover, in the above classes of recursive circuits, upper estimates for the complexity of implementation of some functions and systems of functions used in applications are obtained.


Note: Originally published in Diskretnaya Matematika (2019) 31, №1, 99–110 (in Russian).


  1. Funding: This research was carried out with the financial support of the Russian Foundation for Basic Research (grant no. 18-01-00800).

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Received: 2018-03-26
Revised: 2018-06-03
Published Online: 2020-04-29
Published in Print: 2020-04-28

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