Reduction of Depth of Boolean Networks with a Fan-In Constraint

Franco P. Preparata; David E. Muller; Amnon B. Barak

doi:10.1109/TC.1977.1674864

Reduction of Depth of Boolean Networks with a Fan-In Constraint

Franco P. Preparata
, David E. Muller
, Amnon B. Barak

The Rachel and Selim Benin School of Engineering and Computer Science

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper we present a family of techniques for the design of combinational networks whose objective is the reduction of the number of levels, subject to a constraint on the fan-in of the logic gates. We show that a Boolean expression with n literals and involving the connectives AND and OR can be restructured so that the resulting network of AND and OR gates has depth at most C_l log₂ n + δ, where δ < 0.415 and C_l is 1.81, 1.38, 1.18, and 1 for maximum fan-in l of 2, 3, 4, and 5, respectively. If we additionally require that the amount of equipment of the resulting network be bounded by a linear function of n, it is possible to bound the depth by 2 log₂ n with a fan-in of at most 3.

Original language	English
Pages (from-to)	474-479
Number of pages	6
Journal	IEEE Transactions on Computers
Volume	C-26
Issue number	5
DOIs	https://doi.org/10.1109/TC.1977.1674864
State	Published - May 1977

Keywords

Boolean expressions
combinational networks
computational complexity
design algorithms
fan-in
network depth
number of levels
parallel computation

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10.1109/TC.1977.1674864

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title = "Reduction of Depth of Boolean Networks with a Fan-In Constraint",

abstract = "In this paper we present a family of techniques for the design of combinational networks whose objective is the reduction of the number of levels, subject to a constraint on the fan-in of the logic gates. We show that a Boolean expression with n literals and involving the connectives AND and OR can be restructured so that the resulting network of AND and OR gates has depth at most Cl log2 n + δ, where δ < 0.415 and Cl is 1.81, 1.38, 1.18, and 1 for maximum fan-in l of 2, 3, 4, and 5, respectively. If we additionally require that the amount of equipment of the resulting network be bounded by a linear function of n, it is possible to bound the depth by 2 log2 n with a fan-in of at most 3.",

keywords = "Boolean expressions, combinational networks, computational complexity, design algorithms, fan-in, network depth, number of levels, parallel computation",

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year = "1977",

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journal = "IEEE Transactions on Computers",

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T1 - Reduction of Depth of Boolean Networks with a Fan-In Constraint

AU - Preparata, Franco P.

AU - Muller, David E.

AU - Barak, Amnon B.

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AB - In this paper we present a family of techniques for the design of combinational networks whose objective is the reduction of the number of levels, subject to a constraint on the fan-in of the logic gates. We show that a Boolean expression with n literals and involving the connectives AND and OR can be restructured so that the resulting network of AND and OR gates has depth at most Cl log2 n + δ, where δ < 0.415 and Cl is 1.81, 1.38, 1.18, and 1 for maximum fan-in l of 2, 3, 4, and 5, respectively. If we additionally require that the amount of equipment of the resulting network be bounded by a linear function of n, it is possible to bound the depth by 2 log2 n with a fan-in of at most 3.

KW - Boolean expressions

KW - combinational networks

KW - computational complexity

KW - design algorithms

KW - fan-in

KW - network depth

KW - number of levels

KW - parallel computation

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Reduction of Depth of Boolean Networks with a Fan-In Constraint

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Keywords

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