Algèbre de Boole (logique)

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

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

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 polyno ...

Association for Computing Machinery2024

Algebraic and Boolean Methods for SFQ Superconducting Circuits

Giovanni De Micheli, Alessandro Tempia Calvino

Rapid single-flux quantum (RSFQ) is one of the most advanced and promising superconducting logic families, offering exceptional energy efficiency and speed. RSFQ technology requires delay registers (DFFs) and splitter cells to satisfy the path-balancing an ...

2024

Succinct ordering and aggregation constraints in algebraic array theories

Viktor Kuncak, Rodrigo Raya

We discuss two extensions to a recently introduced theory of arrays, which are based on considerations coming from the model theory of power structures. First, we discuss how the ordering relation on the index set can be expressed succinctly by referring t ...

Elsevier Science Inc2024

On algebraic array theories

Viktor Kuncak, Rodrigo Raya

Automatic verification of programs manipulating arrays relies on specialised decision procedures. A methodology to classify the theories handled by these procedures is introduced. It is based on decomposition theorems in the style of Feferman and Vaught. T ...

Elsevier Science Inc2023

Lattice packings through division algebras

Nihar Prakash Gargava

In this text, we will show the existence of lattice packings in a family of dimensions by employing division algebras. This construction is a generalization of Venkatesh's lattice packing result Venkatesh (Int Math Res Notices 2013(7): 1628-1642, 2013). In ...

SPRINGER HEIDELBERG2023

Improving Standard-Cell Design Flow using Factored Form Optimization

Giovanni De Micheli, Alessandro Tempia Calvino

Factored form is a powerful multi-level representation of a Boolean function that readily translates into an implementation of the function in CMOS technology. In particular, the number of literals in a factored form correlates strongly with the number of ...

IEEE2023

Mechanism balancing taxonomy

Simon Nessim Henein, Florent Cosandier, Hubert Pierre-Marie Benoît Schneegans

The balancing of mechanisms consists in distributing their moving masses, inertias, and elastic components in order to achieve key mechanical properties, such as the elimination of the shaking forces and moments exported onto their supporting structure or ...

2023

Algèbre de Boole (logique)

Graph Chatbot

Scalable Logic Rewriting Using Don’t Cares

In Medio Stat Virtus: Combining Boolean and Pattern Matching

Orthologic with Axioms

Algebraic and Boolean Methods for SFQ Superconducting Circuits

Additive and geometric transversality of fractal sets in the integers

Succinct ordering and aggregation constraints in algebraic array theories

On algebraic array theories

Lattice packings through division algebras

Improving Standard-Cell Design Flow using Factored Form Optimization

Mechanism balancing taxonomy

Scalable Logic Rewriting Using Don’t Cares

In Medio Stat Virtus: Combining Boolean and Pattern Matching

Orthologic with Axioms

Algebraic and Boolean Methods for SFQ Superconducting Circuits

Additive and geometric transversality of fractal sets in the integers

Succinct ordering and aggregation constraints in algebraic array theories

On algebraic array theories

Lattice packings through division algebras

Improving Standard-Cell Design Flow using Factored Form Optimization

Mechanism balancing taxonomy