Concept

Boolean ring

Related publications (32)

On the Number of Containments in P-free Families

A subfamily {F-1, F-2, ..., F-vertical bar P vertical bar} subset of F is a copy of the poset P if there exists a bijection i : P -> {F-1, F-2, ..., F-vertical bar P vertical bar}, such that p

Springer2019

Forbidden induced subposets of given height

Istvan Tomon

Let P be a partially ordered set. The function La* (n, P) denotes the size of the largest family F subset of 2([n]) that does not contain an induced copy of P. It was proved by Methuku and Palvolgyi that there exists a constant C-P (depending only on P) su ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2019

The Complexity of Self-Dual Monotone 7-Input Functions

Giovanni De Micheli, Mathias Soeken, Eleonora Testa, Winston Jason Haaswijk

The study of the complexity of Boolean functions has recently found applications in logic synthesis and optimization algorithms, as for instance in logic rewriting. Previous works have focused on the minimum length of Boolean chains for functions up to 5 i ...

2019

A Hybrid Method for Spectral Translation Equivalent Boolean Functions

Giovanni De Micheli, Mathias Soeken, Eleonora Testa

The equivalence of Boolean functions with respect to five invariance (aka translation) operations has been well considered with respect to the Rademacher-Walsh spectral domain. In this paper, we introduce a hybrid approach that uses both the Reed-Muller an ...

IEEE2019

Scalable Boolean Methods in a Modem Synthesis Flow

Giovanni De Micheli, Mathias Soeken, Pierre-Emmanuel Julien Marc Gaillardon, Luca Gaetano Amarù, Eleonora Testa

With the continuous push to improve Quality of Results (QoR) in EDA, Boolean methods in logic synthesis have been recently drawing the attention of researchers. Boolean methods achieve better QoR than algebraic methods but require higher computational cost ...

IEEE2019

Exact Synthesis of Boolean Functions in Majority-of-five Forms

Giovanni De Micheli, Mathias Soeken, Winston Jason Haaswijk, Zhufei Chu

Recent studies show that majority-based logic synthesis is beneficial for both traditional and nanotechnology digital designs. However, most of the existing synthesis algorithms for majority logic generate majority-of-three (M-3) networks. The optimization ...

IEEE2019

SAT-Based Exact Synthesis for Multi-Level Logic Networks

Winston Jason Haaswijk

Today, the design of electronic systems is largely automated. The practice of using software automation technologies for the design of electronic hardware is commonly referred to as Electronic Design Automation (EDA). EDA comprises a large set of tools, fr ...

EPFL2019

Nonsilicon, Non-von Neumann Computing—Part I

Giovanni De Micheli

Majority-inverter graphs (MIGs) are a logic representation with remarkable algebraic and Boolean properties that enable efficient logic optimizations beyond the capabilities of traditional logic representations. Further, since many nano-emerging technologi ...

IEE2018

Size Optimization of MIGs with an Application to QCA and STMG Technologies

Giovanni De Micheli, Mathias Soeken, Luca Gaetano Amarù, Eleonora Testa, Heinz Riener

ASSOC COMPUTING MACHINERY2018

Functional Decomposition Using Majority

Giovanni De Micheli, Mathias Soeken, Zhufei Chu

Typical operators for the decomposition of Boolean functions in state-of-the-art algorithms are AND, exclusive-OR (XOR), and a 2-to-1 multiplexer (MUX). We propose a logic decomposition algorithm that uses the majority-of-three (MAJ) operation. Such decomp ...

ASSOC COMPUTING MACHINERY2018

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