Cubelike graphs are the Cayley of elementary Abelian group ${\mathbb{Z}}_{2}^{n}$ (e.g., hypercube is a cubelike graph). We study perfect state transfer between two particles in quantum networks modeled by large class graphs. This generalizes results Christandl et al. [Phys. Rev. Lett. 92, 187902 (2004)] and Facer A (2008)].

Several problems in digital logic can be conveniently approached the spectral domain. In this paper we show that Walsh spectrum of Boolean functions analyzed by looking at algebraic properties a class Cayley graphs associated with functions. We use idea to investigate certain special

In this paper, we prove that bent functions can be precisely characterized in terms of a special class strongly regular graphs, thus providing positive answer to question raised the paper by A. Bernasconi and B. Codenotti (1999).

The 2-SPP networks are three-level EXOR-AND-OR forms, with EXOR gates being restricted to fan-in 2. This paper presents a heuristic algorithm for the synthesis of these in form that is fully testable stuck-at fault model (SAFM). extends EXPAND-IRREDUNDANT-REDUCE paradigm ESPRESSO mode, and it iterates local minimization reshape solution until no further improvement can be achieved. could escape from minima using LAST_GASP-like procedure. Moreover, testability under SAFM studied, notion...

We investigate restructuring techniques based on decomposition/factorization, with the objective to move critical signals toward output while minimizing area. A specific application is synthesis for minimum switching activity (or high performance), area penalty, where decompositions respect variables are needed (the ones of highest example). In this paper we describe new types factorization that extend Shannon cofactoring and projection functions change Hamming distance original minterms...

Set accumulators are cryptographic primitives used to represent arbitrarily large sets of elements with a single constant-size value and efficiently verify whether belongs that set. Accumulators support the generation membership proofs, meaning they can certify presence given among In this paper we present an overview theoretical concepts underlying set accumulators, compare most popular constructions from complexity perspective, survey number their applications related blockchain...

Quantum computing sets the foundation for new ways of designing algorithms, thanks to peculiar properties inherited by quantum mechanics. The exploration this paradigm faces challenges concerning which field speedup can be achieved. Toward finding solutions, looking design subroutines that are more efficient than their classical counterpart poses solid pillars powerful algorithms. Herewith, we delve into a grounding subroutine, computation variance, whose usefulness spaces across different...

Abstract The increasing adoption of tokens on the Ethereum blockchain has given rise to many distinct economic communities whose activity history is publicly accessible. In this paper we study fungible and non-fungible tokens, regulated, respectively, by ERC-20 ERC-721 standards. particular, focus token transfers consider top 100 largest ecosystems number transfers, modeling them as networks where nodes correspond participants edges represent transfers. We analyze their main topological...

In this paper we propose a novel approach to the synthesis of minimal-sized lattices, based on decomposition logic functions. Since allows obtain circuits with smaller area, our idea is decompose Boolean functions separate according P-circuits scheme, and then implement decomposed blocks physically separated regions in single lattice. Experimental results show that about 35% considered benchmarks achieve area when implemented using proposed for switching an average gain at least 24%.

We investigate restructuring techniques based on decomposition/factorization, with the objective to move critical signals toward output while minimizing area. A specific application is synthesis for minimum switching activity (or high performance), area penalty, where decompositions respect variables are needed (the ones of highest example). In this paper we describe new types factorization that extend Shannon cofactoring and projection functions change Hamming distance original minterms...

We propose an approximate logic synthesis heuristic for synthesizing a 2-SPP circuit under given error rate threshold. circuits are three-level EXOR-AND-OR forms with EXOR gates restricted to fan-in 2. They represent direct generalization of SOP forms, obtained generalizing cubes "2-pseudocubes" where literals in may be replaced by 2-EXOR factors 2-pseudocubes. discuss and experimentally evaluate two different measures the error: bit threshold minterm The first metric considers overall...

Abstract In the Bitcoin protocol, dust refers to small amounts of currency that are lower than fee required spend them in a transaction. Although “economically irrational”, is commonly used for achieving unconventional side effects, rather exchanging value. For instance, might be linked on-chain services or malicious activity, such as attacks attempting break users’ pseudonymity. To study this phenomenon, paper presents an depth analysis transactions involving dust, showing how created and...

We exploit the "regularity" of Boolean functions with purpose decreasing time for constructing minimal three-level expressions, in sum pseudoproducts (SPP) form recently developed. The regularity a function f n variables can be expressed by an autosymmetry degree k (with 0 /spl les/ n). = means no regularity, that is we are not able to provide any advantage over standard synthesis. For ges/ 1 said autosymmetric, and new f/sub k/ depending on - only, called restriction f, identified...

This paper introduces a new bounded multi-level algebraic form, called projected sum of products (P-SOP), based on projections minimal SOP forms onto subsets the Boolean space. After standard two-level logic minimization, this technique can be used as very fast postprocessing step for further minimizing circuit area, increasing depth network by only constant value. The proposed synthesis algorithms have been implemented and tested with interesting results, which show how about 75% Espresso...

We define and study a new class of regular Boolean functions called D-reducible. A D-reducible function, depending on all its n input variables, can be studied synthesized in space dimension strictly smaller than . show that the D-reducibility property efficiently tested, time polynomial representation f , is, an initial SOP form function decomposed, giving rise to logic form, we have DredSOP. This is shown here generally corresponding minimum form. Our experiments also great number...

In this paper we study the switching lattice synthesis of a special class regular Boolean functions called D-reducible functions. are whose points completely contained in an affine space A strictly smaller than whole cube {0, 1} <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> . The D-reducibility function f can be exploited process: idea is to independently find implementations for characteristic subspace and projection onto A, compose...