A Novel Basis for Logic Rewriting

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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. ...

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 ...

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 ...

Electronic devices play an irreplaceable role in our lives. With the tightening time to market, exploding demand for computing power, and continuous desire for smaller, faster, less energy-consuming, and lower-cost chips, computer-aided design for electron ...

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 ...

By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...

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 ...

Individual transistors based on emerging reconfigurable nanotechnologies exhibit electrical conduction for both types of charge carriers. These transistors (referred to as Reconfigurable Field-Effect Transistors (RFETs)) enable dynamic reconfiguration to d ...

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 ...

We survey lower-bound results in complexity theory that have been obtained via newfound interconnections between propositional proof complexity, boolean circuit complexity, and query/communication complexity. We advocate for the theory of total search prob ...

Approximate logic synthesis is an emerging field that tolerates errors in the synthesized logic circuits for better optimization quality. Indeed, in many computing problems, the requirement of preserving the exact functionality either results in unnecessar ...

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 ...

The beginning of 21st century provided us with many answers about how to reach the channel capacity. Polarization and spatial coupling are two techniques for achieving the capacity of binary memoryless symmetric channels under low-complexity decoding algor ...

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 ...

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 ...

Logic resynthesis is the problem of finding a dependency function to re-express a given Boolean function in terms of a given set of divisor functions. In this paper, we study logic resynthesis of majority-based circuits, which is motivated by the increasin ...

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 ...

Many natural optimization problems are NP-hard, which implies that they are probably hard to solve exactly in the worst-case. However, it suffices to get reasonably good solutions for all (or even most) instances in practice. This paper presents a new algo ...

We propose a flow for automated quantum compila- tion. Our flow takes a Boolean function implemented in Python as input and translates it into a format appropriate for reversible logic synthesis. We focus on two quantum compilation tasks: uniform state pre ...

Adiabatic quantum-flux-parametron (AQFP) circuits are a family of superconducting electronic (SCE) circuits that have recently gained growing interest due to their low-energy consumption, and may serve as alternative technology to overcome the down-scaling ...

A Novel Basis for Logic Rewriting

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Scalable Logic Rewriting Using Don’t Cares

In Medio Stat Virtus: Combining Boolean and Pattern Matching

Algebraic and Boolean Methods for SFQ Superconducting Circuits

Contemporary Logic Synthesis: with an Application to AQFP Circuit Optimization

Orthologic with Axioms

Additive and geometric transversality of fractal sets in the integers

Improving Standard-Cell Design Flow using Factored Form Optimization

Utilizing XMG-based Synthesis to Preserve Self-Duality for RFET-Based Circuits

Equivalence Checking for Orthocomplemented Bisemilattices in Log-Linear Time

Proofs, Circuits, and Communication

Logic Synthesis From Incomplete Specifications Using Disjoint Support Decomposition

Formula Normalizations in Verification

Symmetry in design and decoding of polar-like codes

Three-Input Gates for Logic Synthesis

A Majority Lemma for Randomised Query Complexity

Logic Resynthesis of Majority-Based Circuits by Top-Down Decomposition

Preserving Self-Duality During Logic Synthesis for Emerging Reconfigurable Nanotechnologies

Learning from survey propagation: a neural network for MAX-E-3-SAT

From Boolean functions to quantum circuits: A scalable quantum compilation flow in C++

Algebraic and Boolean Optimization Methods for AQFP Superconducting Circuits