Publications associées à Logique algébrique

Preserving Self-Duality During Logic Synthesis for Emerging Reconfigurable Nanotechnologies

Giovanni De Micheli, Heinz Riener, Shubham Rai, Akash Kumar

Emerging reconfigurable nanotechnologies allow the implementation of self-dual functions with a fewer number of transistors as compared to traditional CMOS technologies. To achieve better area results for Reconfigurable Field-Effect Transistors (RFET)-base ...

IEEE2021

Three-Input Gates for Logic Synthesis

Giovanni De Micheli, Mathias Soeken, Dewmini Sudara Marakkalage, Eleonora Testa, Heinz Riener

Most logic synthesis algorithms work on graph representations of logic functions with nodes associated with arbitrary logic expressions or simple logic functions and iteratively optimize such graphs. While recent multilevel logic synthesis efforts focused ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Advanced Functional Decomposition Using Majority and Its Applications

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 the 2-to-1 multiplexer (MUX). We propose a logic decomposition algorithm that uses the majority-of-three (MAJ) operation. Such a de ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Unique decomposition of homogeneous languages and application to isothetic regions

Nicolas René Jean Ninin

A language is said to be homogeneous when all its words have the same length. Homogeneous languages thus form a monoid under concatenation. It becomes freely commutative under the simultaneous actions of every permutation group G(n) on the collection of ho ...

2019

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

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 ...

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 ...

IEEE2018

Exact Synthesis of Majority-Inverter Graphs and Its Applications

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

We propose effective algorithms for exact synthesis of Boolean logic networks using satisfiability modulo theories (SMT) solvers. Since exact synthesis is a difficult problem, it can only be applied efficiently to very small functions, having up to 6 varia ...

Ieee-Inst Electrical Electronics Engineers Inc2017

Algebraic and topological methods in combinatorics

Adrian Claudiu Valculescu

The present thesis deals with problems arising from discrete mathematics, whose proofs make use of tools from algebraic geometry and topology. The thesis is based on four papers that I have co-authored, three of which have been published in journals, and o ...

EPFL2017

A Novel Basis for Logic Rewriting

Giovanni De Micheli, Mathias Soeken, Pierre-Emmanuel Julien Marc Gaillardon, Luca Gaetano Amarù, Winston Jason Haaswijk

Given a set of logic primitives and a Boolean function, exact synthesis finds the optimum representation (e.g., depth or size) of the function in terms of the primitives. Due to its high computational complexity, the use of exact synthesis is limite ...

Ieee2017