Publications related to Boolean ring

In Medio Stat Virtus: Combining Boolean and Pattern Matching

Giovanni De Micheli, Alessandro Tempia Calvino, Gianluca Radi

Technology mapping transforms a technology-independent representation into a technology-dependent one given a library of cells. This process is performed by means of local replacements that are extracted by matching sections of the subject graph to library ...

IEEE2024

Formula Normalizations in Verification

Viktor Kuncak, Simon Guilloud, Mario Bucev, Dragana Milovancevic

We propose a new approach for normalization and simplification of logical formulas. Our approach is based on algorithms for lattice-like structures. Specifically, we present two efficient algorithms for computing a normal form and deciding the word problem ...

2023

Equivalence Checking for Orthocomplemented Bisemilattices in Log-Linear Time

Viktor Kuncak, Simon Guilloud

We present a quasilinear time algorithm to decide the word problem on a natural algebraic structures we call orthocomplemented bisemilattices, a subtheory of boolean algebra. We use as a base a variation of Hopcroft, Ullman and Aho algorithm for tree isomo ...

Springer2022

Stabilized isogeometric discretizations on trimmed and union geometries, and weak imposition of the boundary conditions for the Darcy flow

Riccardo Puppi

Modern manufacturing engineering is based on a ``design-through-analysis'' workflow. According to this paradigm, a prototype is first designed with Computer-aided-design (CAD) software and then finalized by simulating its physical behavior, which usually i ...

EPFL2022

BLOOM: Bimodal Lattice One-out-of-Many Proofs and Applications

Ngoc Khanh Karol Nguyen

We give a construction of an efficient one-out-of-many proof system, in which a prover shows that he knows the pre-image for one element in a set, based on the hardness of lattice problems. The construction employs the recent zero-knowledge framework of Ly ...

SPRINGER INTERNATIONAL PUBLISHING AG2022

A Majority Lemma for Randomised Query Complexity

Mika Tapani Göös, Gilbert Théodore Maystre

We show that computing the majority of n copies of a boolean function g has randomised query complexity R(Maj∘gⁿ) = Θ(n⋅R ̅_{1/n}(g)). In fact, we show that to obtain a similar result for any composed function f∘gⁿ, it suffices to prove a sufficiently stro ...

Schloss Dagstuhl - Leibniz-Zentrum für Informatik2021

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

Enumerating Optimal Quantum Circuits using Spectral Classification

Giovanni De Micheli, Mathias Soeken, Giulia Meuli

This work targets fault-tolerant quantum computing and focuses on the problem of mapping reversible circuits into the Clifford+T quantum gate library. We present an automatically-generated database containing minimal-cost quantum circuits for Boolean funct ...

IEEE2020

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

Data Structures and Algorithms for Logic Synthesis in Advanced Technologies

Eleonora Testa

Logic synthesis is a key component of digital design and modern EDA tools; it is thus an essential instrument for the design of leading-edge chips and to push the limits of their performance. In the last decades, the electronic circuits community has evolv ...

EPFL2020

On the Number of Containments in P-free Families

Abhishek Methuku

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

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

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

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