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Structural Rewriting in XOR-Majority Graphs

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Scalable Logic Rewriting Using Don’t Cares

Giovanni De Micheli, Alessandro Tempia Calvino

Logic rewriting is a powerful optimization technique that replaces small sections of a Boolean network with better implementations. Typically, exact synthesis is used to compute optimum replacement on-the-fly, with possible support for Boolean don't cares. ...

2024

Orthologic with Axioms

Viktor Kuncak, Simon Guilloud

We study the proof theory and algorithms for orthologic, a logical system based on ortholattices, which have shown practical relevance in simplification and normalization of verification conditions. Ortholattices weaken Boolean algebras while having po ...

2024

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We present LISA, a proof system and proof assistant for constructing proofs in schematic first-order logic and axiomatic set theory. The logical kernel of the system is a proof checker for first-order logic with equality and schematic predicate and fun ...

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

At the FSE conference of ToSC 2018, Kranz et al. presented their results on shortest linear programs for the linear layers of several well known block ciphers in literature. Shortest linear programs are essentially the minimum number of 2-input xor gates r ...

2021

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 ...

2021

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

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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

2019

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