Anna Bernasconi

• University of Pisa

In the classical CMOS technology, EXOR gates are considered expensive and impractical. Recently, the growing relevance of cryptography-related applications and emerging technologies has revived the interest in EXOR gates. In this contexts, it is therefore important to consider network representations that assume EXOR gates explicitly, since the non...

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 the communities of Ethereum fungible and non-fungible tokens, regulated, respectively, by the ERC-20 and ERC-721 standards. In particular, we focus on token transfers...

Quantum computing sets the foundation for new ways of designing algorithms, thanks to the peculiar properties inherited by quantum mechanics. The exploration of this new paradigm faces new challenges concerning which field quantum speedup can be achieved. Toward finding solutions, looking for the design of quantum subroutines that are more efficien...

Bi-decomposition rewrites logic functions as the composition of simpler components. It is related to Boolean division, where a given function is rewritten as the product of a divisor and a quotient, but bi-decomposition can be defined for any Boolean operation of two operands. The key questions are how to find a good divisor and then how to compute...

Over the past few years, we observed a rethinking of classical artificial intelligence algorithms from a quantum computing perspective. This trend is driven by the peculiar properties of quantum mechanics, which offer the potential to enhance artificial intelligence capabilities, enabling it to surpass the constraints of classical computing. Howeve...

The transparent nature of public blockchain systems allows for unprecedented access to economic community data. Examples of such communities are the fungible token networks created by the ERC-20 standard on the Ethereum protocol. In this paper we study ERC-20 token networks, where nodes represent users and edges represent fungible token transfers b...

We propose an efficient quantum subroutine for matrix multiplication that computes a state vector encoding the entries of the product of two matrices in superposition. The subroutine exploits efficient state preparation techniques and shows a potential speed-up with respect to classical methods. The most important benefit of our subroutine is that...

Over the past few years, we observed a rethinking of classical artificial intelligence algorithms from a quantum computing perspective. This trend is driven by the peculiar properties of quantum mechanics, which offer the potential to enhance artificial intelligence capabilities, enabling it to surpass the constraints of classical computing. Howeve...

In the Bitcoin protocol, dust refers to small amounts of currency that are lower than the fee required to spend them in a transaction. Although “economically irrational”, dust is commonly used for achieving unconventional side effects, rather than exchanging value. For instance, dust might be linked to on-chain services or to malicious activity, su...

In this paper we study Boolean functions that exhibit two different XOR-based regularities (i.e., autosymmetry and D-reducibility) at the same time. XOR-based regularities can be exploited for the efficient computation of multiplicative complexity of a Boolean function f (i.e., the minimum number of AND gates that are necessary and sufficient to re...

Dust refers to the amounts of cryptocurrency that are smaller than the fees required to spend them in a transaction. Due to its “economically irrational” nature, dust is often used to achieve some external side effect, rather than exchanging value. In this paper we study this phenomenon by conducting an analysis of dust creation and consumption in...

The promise of quantum computation to achieve a speedup over classical computation led to a surge of interest in exploring new quantum algorithms for data analysis problems. Feature Selection, a technique that selects the most relevant features from a dataset, is a critical step in data analysis. With several Quantum Feature Selection techniques pr...

Quantum computing is a promising paradigm based on quantum theory for performing fast computations. Quantum algorithms are expected to surpass their classical counterparts in terms of computational complexity for certain tasks, including machine learning. In this paper, we design, implement, and evaluate three hybrid quantum k-Means algorithms, exp...

With the rapid increasing availability of information and popularization of mobility devices, trajectories have become more complex in their form. Trajectory data is now high dimensional, and often associated with heterogeneous sources of semantic data, that are called Multiple Aspect Trajectories. The high dimensionality and heterogeneity of these...

In the last years, we have witnessed the increasing usage of machine learning technologies. In parallel, we have observed the raise of quantum computing, a paradigm for computing making use of quantum theory. Quantum computing can empower machine learning with theoretical properties allowing to overcome the limitations of classical computing. The t...

XOR-AND Graphs (XAGs) are an enrichment of the classical AND-Inverter Graphs (AIGs) with XOR nodes. In particular, XAGs are networks composed by ANDs, XORs, and inverters. Besides several emerging technologies applications, XAGs are often exploited in cryptography-related applications based on the multiplicative complexity of a Boolean function. Th...

We propose a new three-level XOR-AND-XOR form for autosymmetric functions, called XORAX expression. In general, a Boolean function f over n variables is k-autosymmetric if it can be projected onto a smaller function fk, which depends on n-k variables only. We show that XORAX expressions can ease the reversible synthesis of autosymmetric functions,...

In many blockchain networks, light nodes (e.g. mobile clients) with few computational resources must rely on more powerful full nodes to retrieve transactions from the chain. However, in this untrusted environment a malicious full node could deliver altered or incomplete information, requiring query authentication techniques to ensure the integrity...

In reaction systems, preimages and nth ancestors are sets of reactants leading to the production of a target set of products in either 1 or n steps, respectively. Many computational problems on preimages and ancestors, such as finding all minimum-cardinality nth ancestors, computing their size or counting them, are intractable. In this paper, we ch...

Approximate synthesis is a recent trend in logic synthesis where one changes some outputs of a logic specification, within the error tolerance of a given application, to reduce the complexity of the final implementation. We attack the problem by exploiting the allowed flexibility in order to maximize the regularity of the specified Boolean function...

Switching lattices are two-dimensional arrays composed of two or four-terminals switches organized as a crossbar array. The idea of using regular two-dimensional arrays of switches for Boolean function implementation was proposed by Akers in 1972. Recently, with the advent of a variety of emerging nanoscale technologies, lattices have found a renew...

Switching lattices are two-dimensional arrays of four-terminal switches proposed in a seminal paper by Akers in 1972 to implement Boolean functions. Recently, with the advent of a variety of emerging nanoscale technologies based on regular arrays of switches, synthesis methods targeting lattices of multi-terminal switches have found a renewed inter...

A non classical approach to the logic synthesis of Boolean functions based on switching lattices is considered, for which deriving a feasible layout has not been previously studied. All switches controlled by the same literal must be connected together and to an input lead of the chip, and the layout of such connections must be realized in superimp...

Projected Sums of Products (PSOPs) are a Generalized Shannon Decomposition (GSD) with remainder that restructures a logic function into three logic blocks corresponding to a logic bi-decomposition plus a reminder generated by a cofactoring function. In this paper we discuss a Boolean synthesis technique for PSOPs, which exploits the fact that the r...

Multi-terminal switching lattices are typically exploited for modeling switching nano-crossbar arrays that lead to the design and construction of emerging nanocomputers. Typically, the circuit is represented on a single lattice composed by four-terminal switches. In this paper, we propose a two-layer model in order to further minimize the area of r...

In this paper we propose a novel approach to the synthesis of minimal-sized lattices, based on the decomposition of logic functions. Since the decomposition allows to obtain circuits with a smaller area, our idea is to decompose the Boolean functions according to generalizations of the classical Shannon decomposition, then generate the lattices for...

Beyond CMOS, new technologies are emerging to extend electronic systems with features unavailable to silicon-based devices. Emerging technologies provide new logic and interconnection structures for computation, storage and communication that may require new design paradigms, and therefore trigger the development of a new generation of design autom...

In this paper we study the switching lattice synthesis of a special class of regular Boolean functions called D-reducible functions. D-reducible functions are functions whose points are completely contained in an affine space A strictly smaller than the whole Boolean cube {0, 1} n . The D-reducibility of a function ƒ can be exploited in the lattice...

Zero-Suppressed Binary Decision Diagrams (ZDDs) are widely used data structures for representing and handling combination sets and Boolean functions. In particular, ZDDs are commonly used in CAD for the synthesis and verification of integrated circuits. The purpose of this article is to design an error-resilient version of this data structure: a se...

In this paper we study the problem of characterizing and exploiting the complete flexibility of a special logic architecture, called P-circuits, which realize a Boolean function by projecting it onto overlapping subsets given by a generalized Shannon decomposition. P-circuits are used to restructure logic by pushing some signals towards the outputs...

This paper discusses the error resilience of zero-suppressed binary decision diagrams (ZDDs), which are a particular family of ordered binary decision diagrams used for representing and manipulating combination sets. More precisely, we design a new ZDD canonical form, called index-resilient reduced ZDD, such that a faulty index can be reconstructed...

We propose an approximate logic synthesis heuristic for synthesizing a 2-SPP circuit under a given error rate threshold. 2-SPP circuits are three-level EXOR-AND-OR forms with EXOR gates restricted to fan-in 2. They represent a direct generalization of SOP forms, obtained generalizing cubes to '2-pseudocubes' where literals in cubes may be replaced...

Ordered Binary Decision Diagrams (OBDDs) are a data structure that is used in an increasing number of fields of Computer Science (e.g., logic synthesis, program verification, data mining, bioinformatics, and data protection) for representing and manipulating discrete structures and Boolean functions. The purpose of this paper is to study the error...

Autosymmetric and dimension reducible functions are classes of Boolean functions whose regular structure can be exploited by synthesis algorithms in order to reduce the minimization time and to derive more compact algebraic forms. In this paper we first propose a generalization of these classes of functions to the multiple-valued logic framework. T...

In this paper we define and study the properties of a generalized Shannon expansion on non-disjoint subsets of the Boolean space. This expansion consists in projecting the original function onto several overlapping subsets. Since the logic can be distributed among the projection subsets, input combinations asserted by a subset may be exploited as d...

Generalized Shannon decomposition with remainder restructures a logic function into subsets of points defined by the generalized cofactors with a remainder, yielding three logic blocks. EXOR-Projected Sums of Products (EP-SOPs) are an important form of such decomposition. In this paper we propose a Boolean synthesis technique for EP-SOPs, more gene...

Ordered Binary Decision Diagrams (OBDDs) are a widely used data structure for Boolean function manipulation. In particular, OBDDs are commonly used in CAD for the synthesis and verification of integrated circuits. The purpose of this paper is to design an error resilient version of this data structure, i.e., self-repairing OBDDs.We describe some st...

In this paper, we investigate how to use the complete flexibility of P-circuits, which realize a Boolean function by projecting it onto overlapping subsets given by a generalized Shannon decomposition. It is known how to compute the complete flexibility of P-circuits, but the algorithms proposed so far for its exploitation do not guarantee to find...

In this paper we define and study the properties of projected don't cares, a category of don't cares dynamically built by the minimization algorithm during the synthesis phase. Our target is to exploit projected don't cares properties in order to obtain more compact networks. In particular, we show the use of projected don't care conditions in two...

Boolean functional decomposition techniques built on top of Shannon cofactoring are applied to obtain specialized 4-level forms called Projected Circuits, or P-circuits. We describe their minimization by heuristic and guaranteed approximation algorithms exploiting structural don't care conditions, and prove properties for special cases about cost e...

Given a Boolean function f on n variables, a Disjoint Sum-of-Products (DSOP) of f is a set of products (ANDs) of subsets of literals whose sum (OR) equals f, such that no two products cover the same minterm of f. DSOP forms are a special instance of partial DSOPs, i.e. the general case where a subset of minterms must be covered exactly once and the...

Boolean functional decomposition techniques built on top of Shannon cofactoring have been discussed in various applications of logic synthesis targeting reductions in area, delay and power. In this paper we investigate a generalization of decomposition based on Shannon cofactoring by means of non-orthonormal projection functions. We provide an appr...

Auto symmetric functions are a class of Boolean functions whose regular structure can be exploited by synthesis algorithms in order to reduce the minimization time and to derive more compact algebraic forms. In this paper we propose a generalization of this class of functions to the multiple-valued logic framework. We also study the spectral proper...

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 and synthesized in a space of dimension strictly smaller than n. We show that the D-reducibility property can be efficiently tested, in time polynomial in the representation of f, that is, a...

This chapter investigates some restructuring techniques based on decom-position and factorization, with the objective to move critical signals toward the output while minimizing area. A speci c application is synthesis for minimum switching activity (or high performance), with minimum area penalty, where decom-positions with respect to speci c crit...

In logic synthesis, the “regularity” of a Boolean function can be exploited with the purpose of decreasing the cost of the corresponding algebraic expression or its minimization time. In this paper we study the synthesis of a class of regular Boolean functions called D-reducible. We propose two compact and testable representations of D-reducible no...

In this paper we introduce new algebraic forms, SOP + and DSOP + , to represent functions f:{0,1} n →ℕ, based on arithmetic sums of products. These expressions are a direct generalization of the classical SOP and DSOP forms. We propose optimal and heuristic algorithms for minimal SOP + and DSOP + synthesis. We then show how the DSOP + form can be e...

We investigate a form of logic decomposition that generates a 2SPP-P-circuit, which includes two blocks representing the projected subfunctions obtained by Shannon cofactoring with respect to a chosen variable, and a block representing the intersection of the projections. The three blocks are implemented as minimal 2-SPP forms (XOR-ANDOR with XOR r...

We investigate restructuring techniques based on decomposition/factorization, with the objective to move critical signals toward the output while minimizing area. A specific application is synthesis for minimum switching activity (or high performance), with minimum area penalty, where decompositions with respect to specific critical variables are n...

Cubelike graphs are the Cayley graphs of the elementary abelian group (Z_2)^n (e.g., the hypercube is a cubelike graph). We give conditions for perfect state transfer between two particles in quantum networks modeled by a large class of cubelike graphs. This generalizes results of Christandl et al. [Phys. Rev. Lett. 92, 187902 (2004)] and Facer et...

Compact area, low delay and good testability properties are important optimization goals in the synthesis of circuits for Boolean functions. Unfortunately, these goals typically contradict each other. Multi-level circuits are often quite small but can have a long delay, due to their unbounded number of levels. On the other hand, circuits with low d...

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 networks in a form that is fully testable in the stuck-at fault model (SAFM). The algorithm extends the EXPAND-IRREDUNDANT-REDUCE paradigm of ESPRESSO in heuristic mode, and it iter...

Autosymmetric functions exhibit a special type of regularity that can speed-up the minimization process. Based on this autosymmetry, we propose a three level form of logic synthesis, called ORAX (EXOR-AND-OR), to be compared with the standard minimal SOP (Sum of Products) form. First we provide a fast ORAX minimization algorithm for autosymmetric...

We propose a new algebraic four-level expression called k-EXOR-projected sum of products (kEP-SOP). The optimization of a kEP-SOP is NP NP -hard, but can be approximated within a fixed performance guarantee in polynomial time. Moreover, fully testable circuits under the stuck-at-fault model can be derived from kEP-SOPs by adding at most a constant...

We investigate relationships between knitting and formal systems. We show how formal languages, grammars, and algorithms give rise to powerful tools that can be used in both descriptive and prescriptive ways that have not yet been fully explored for designing, then knitting, complex patterns. In particular, we generate knitting meta charts, i.e. ab...

We propose a new algebraic four-level expression called k-EXOR-projected sum of products (kEP-SOP). The optimization of a kEP-SOP is NPNP-hard, but can be approximated within a fixed performance guarantee in polynomial time. Moreover, fully testable circuits under the stuck-at-fault model can be derived from kEP-SOPs by adding at most a constant nu...

This paper introduces a new bounded multi-level algebraic form, called projected sum of products (P-SOP), based on projections of minimal SOP forms onto subsets of the Boolean space. After a standard two-level logic minimization, this technique can be used as a very fast postprocessing step for further minimizing the circuit area, increasing the de...

We give a heuristic for Disjoint Sum-of-Products (DSOP) minimization of a Boolean function f , based on a new criterion for product selection. Starting from a Sum-of-Products (SOP) S of f , i.e., a set of cubes covering the 1's of f , we assign a weight w(p) to each product (cube) p in S, where w(p) depends on the intersection of p with the other c...

We define a new algebraic form for Boolean function representation, called EXOR-Projected Sum of Products(EP-SOP), consisting in a four level network that can be easily implemented in practice. Deriving an optimal EP-SOP from an optimal SOP form is a NPNP-hard problem; nevertheless we propose a very efficient approximation algorithm, which returns,...

During synthesis of circuits for Boolean functions area, delay and testability are optimization goals that often contradict each other. Multi-level circuits are often quite small while circuits with low depth are often larger regarding the area requirements. A different optimization goal is good testability which can usually only be achieved by add...

In this paper we investigate the relations between knitting and computer science. We show that the two disciplines share many concepts. Computer science, in particular algorithm theory, can suggest a lot of powerful tools that can be used both in descriptive and prescriptive ways and that apparently have not yet been used for creative knitting. The...

Multi-level logic synthesis yields much more compact expressions of a given Boolean function with respect to standard two-level sum of products (SOP) forms. On the other hand, minimizing an expression with more than two-levels can take a large time. In this paper we introduce a novel algebraic four-level expression, named k-EXOR-projected sum of pr...

In this paper, the authors introduce a new algebraic form for Boolean function representation, called EXOR-projected sum of products (EP-SOP), resulting in a four level network that can be easily implemented in practice. The authors prove that deriving an optimal EP-SOP from an optimal sum of products (SOP) form is a hard problem (NP ^NP-...

Full testability is a desirable property for a minimal logic network. The classical minimal two-level sum of products (SOP) networks are fully testable in some standard fault models. In this paper, the authors investigate the testability of recently introduced three-level logic forms sum of pseudoproducts (SPP), which allow the representation of Bo...

Recently introduced, three-level logic Sum of Pseudoproducts (SPP) forms allow the representation of Boolean functions with much shorter expressions than standard two-level Sum of Products (SOP) forms, or other three-level logic forms. In this paper the testability of circuits derived from SPPs is analyzed. We study testability under the Stuck-At F...

The "regularity" of a Boolean function can be exploited for decreasing its minimization time. It has already been shown that the notion of autosymmetry is a valid measure of regularity, however such a notion has been studied thus far either in the theoretical framework of self-dual Boolean functions, or for the synthesis of a particular family of t...

This paper introduces the notions of balanced and strongly balanced Boolean functions and examines the complexity of these functions using harmonic analysis on the hypercube. The results are applied to derive a lower bound related to AC 0 functions.

The paper presents a heuristic algorithm for the minimization of 2-SPP networks, i.e., three-level EXOR-AND-OR forms with EXOR gates restricted to fan-in 2. Previous works had presented exact algorithms for the minimization of unrestricted SPP networks and of 2-SPP networks. The exact minimization procedures were formulated as covering problems as...

In this paper we characterize 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 and synthesized in a space of dimension strictly smaller than n. A D-reducible function can be efficiently decomposed, giving rise to a new logic form, that we have calle...

The quadratic assignment problem (QAP) is among the hardest combinatorial optimization problems. Very few instances of this problem can be solved in polynomial time. In this paper we address the problem of allocating rooms among people in a suitable shape of corridor with some constraints of undesired neighborhood. We give a linear time algorithm f...

We study the Walsh representation of symmetric functions, with special attention given to the case of symmetric threshold (i.e., symmetric and monotone) functions. The goal is to look at the frequency domain to get a compact description for symmetric threshold functions in the Boolean and multivalued settings.

We exploit the "regularity" of Boolean functions with the purpose of decreasing the time for constructing minimal three-level expressions, in the sum of pseudoproducts (SPP) form recently developed. The regularity of a Boolean function f of n variables can be expressed by an autosymmetry degree k (with 0 ≤ k ≤ n). k = 0 means no regularity, that is...

We study various combinatorial complexity measures of Boolean functions related to some natural arithmetic problems about binary polynomials, that is, polynomials over $$ \mathbb{F}_2 $$ . In particular, we consider the Boolean function deciding whether a given polynomial over $$ \mathbb{F}_2 $$ is squarefree. We obtain an exponential lower bound o...

Sum of Pseudoproducts (SPPs) are three-level network structures that give a good compromise between compact representation and small depth of the resulting circuit. In this paper the testability of circuits derived from SPPs is studied. For SPPs several restricted forms can be consid- ered. While full testability can be proved for some classes, oth...

Following ideas from [Hei83, DFGS91, MT97] and applying the techniques proposed in [May89, KM96, Kuh98], we present a deterministic algorithm for computing the dimension of a polynomial ideal requiring polynomial working space.

Sum of pseudoproducts (SPP) is a three level logic synthesis technique developed in recent years. In this framework we exploit the "regularity" of Boolean functions to decrease minimization time. The main results are: 1) the regularity of a Boolean function f of n variables is expressed by its autosymmetry degree k (with 0 ≤ k ≤ n), where k = 0 mea...