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On the complexity of realizations of Boolean functions in some classes of hypercontact circuits

  • Yury G. Tarazevich EMAIL logo
Published/Copyright: February 13, 2024

Abstract

In the classes EMF(n) of extended matrices over rings of polynomials with idempotent variables, the following subclasses (hypercontact circuits) are defined: HCF(n) (over an arbitrary field F) and HCZ(n) (over the ring of integers), which algebraically extend the class of incident matrices of contact circuits (CC(n)) and realize arbitrary n-place Boolean functions with contact complexity smaller than 322n/2. A lower estimate of the same order is obtained for the corresponding Shannon function in the class HCFq(n) over an arbitrary finite field Fq. For matrices from the class HCZ(n) , we find a physical interpretation in the form of incident-linking matrices of contact-transformer circuits.


Originally published in Diskretnaya Matematika (2022) 34, №3, 90–113 (in Russian).


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Received: 2018-02-18
Revised: 2021-12-24
Published Online: 2024-02-13
Published in Print: 2024-01-29

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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