Asymptotically sharp estimates for the area of multiplexers in the cellular circuit model-Reference-Cited by-同舟云学术

Asymptotically sharp estimates for the area of multiplexers in the cellular circuit model

Published:2024-04-01 Issue:2 Volume:34 Page:103-115
ISSN:0924-9265
Container-title:Discrete Mathematics and Applications
language:en
Short-container-title:

Author:

Lozhkin Sergei A.¹,Zizov Vadim S.¹

Affiliation:

1. Lomonosov Moscow State University , Moscow , Russia

Abstract

Abstract A general cellular circuit of functional and switching elements (CCFSE) is a mathematical model of integral circuits (ICs), which takes into account peculiarities of their physical synthesis. A principal feature of this model distinguishing it from the well-known classes of circuits of gates (CGs) is the presence of additional requirements on the geometry of the circuit which ensure the accounting of the necessary routing resources for IC creation. The complexity of implementation of a multiplexer function of Boolean algebra (FBA) in different classes of circuits has been extensively studied. In the present paper, we give asymptotically sharp upper and lower estimates for the area of a CCFSE implementing a multiplexer FBA of order n. We construct a family of circuit multiplexers of order n of area equal to the halved upper estimate, and provide a method of delivering the corresponding lower estimate.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/dma-2024-0009/pdf

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