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Papers by Enrico Formenti

Research paper thumbnail of Pure reaction automata

Natural computing, May 29, 2024

Research paper thumbnail of Computational Complexity of Rule Distributions of Non-uniform Cellular Automata

Research paper thumbnail of MDDs Boost Equation Solving on Discrete Dynamical Systems

Research paper thumbnail of Decidable Properties of 2D Cellular Automata

Lecture Notes in Computer Science, 2008

In this paper we study some decidable properties of two-dimensional cellular automata (2D CA). Th... more In this paper we study some decidable properties of two-dimensional cellular automata (2D CA). The notion of closingness is generalized to the 2D case and it is linked to permutivity and openness. The major contributions of this work are two deep constructions which ...

Research paper thumbnail of Solving Equations on Discrete Dynamical Systems (Extended version)

arXiv (Cornell University), Apr 30, 2019

Research paper thumbnail of Cellular Automata and Discrete Complex Systems

Research paper thumbnail of Chaotic Behavior of Cellular Automata

Springer eBooks, 2009

Université de Marne la Vallée.

Research paper thumbnail of An Efficient Algorithm Deciding Chaos for Linear Cellular Automata Over (Z/Mz)^N with Applications to Data Encryption

Research paper thumbnail of An Algorithmic Pipeline for Solving Equations over Discrete Dynamical Systems Modelling Hypothesis on Real Phenomena

arXiv (Cornell University), Nov 9, 2022

Research paper thumbnail of Basic Properties for Sand Automata

HAL (Le Centre pour la Communication Scientifique Directe), Sep 1, 2005

Research paper thumbnail of Foreword: asynchronous behavior of cellular automata and discrete models

Natural Computing, Oct 20, 2015

This special issue contains a selection of papers presented at the ‘‘Third International Workshop... more This special issue contains a selection of papers presented at the ‘‘Third International Workshop on Asynchronous Cellular Automata and Asynchronous Discrete Models’’ (ACA 2014), held as a satellite workshop of the 11th International Conference on Cellular Automata for Research and Industry (ACRI 2014) in Krakow (Poland) in September 2014. Six papers were selected and, after an additional review process, five of them have been included in this special issue. They are now presented in an extended and improved form with respect to the already refereed workshop version that appeared in the proceedings of the ACRI 2014 conference. The ACA workshop is devoted to the theme of asynchrony, a hot topic, inside Cellular Automata and other Discrete Models as, for instance, Boolean Networks. Cellular Automata are a well-known formal tool for modeling complex systems; they are considered in many scientific fields and industrial applications. Synchronicity is one of the main features of Cellular Automata evolutions. Indeed, in the most common Cellular Automata framework, all cells are updated simultaneously at each discrete time step by means of a same rule. Recent trends consider the modeling of asynchronous systems based on local and possibly non-uniform interactions. The aim of this workshop is to bring together researchers dealing with the theme of the asynchrony inside Cellular Automata and Discrete Models. Typical, but not exclusive, topics of the workshop are dynamics, complexity and computational issues, emergent properties, models of parallelism and distributed systems, and models of real phenomena. The paper ‘‘Local structure approximation as a predictor of second-order phase transitions in asynchronous cellular automata’’ by Henryk Fukś and Nazim Fates considers aasynchronous elementary cellular automata, that is elementary cellular automata in which each cell independently updates with probability a. By means of an extension of the mean-field approximation technique, the authors study the phase transitions in such automata, i.e., the changes of the dynamical behavior which may occur when the parameter a varies. In the paper ‘‘Supercritical probabilistic cellular automata: How effective is the synchronous updating?’’, PierreYves Louis deals with the issue of quantifying the effectiveness of the parallel updating in probabilistic cellular automata, i.e., cellular automata where the local rule is defined by means of a probability. Two interesting classes of probabilistic cellular automata are considered. An analysis of simulation is presented and shows that the behavior of these classes is nearly asynchronous when transition phase phenomena occur. Boolean Networks model the dynamical interaction of components which take a binary state. They have been & Alberto Dennunzio dennunzio@disco.unimib.it

Research paper thumbnail of Decidable characterizations of dynamical properties for additive cellular automata over a finite abelian group with applications to data encryption

Information Sciences, Jul 1, 2021

Abstract Additive cellular automata over a finite abelian group are a wide class of cellular auto... more Abstract Additive cellular automata over a finite abelian group are a wide class of cellular automata (CA) that are able to exhibit the complex behaviors of general CA and are often exploited for designing applications in different practical contexts. We provide decidable characterizations for Additive CA of the following important properties defining complex behaviors of complex systems: injectivity , surjectivity, equicontinuity, sensitivity to the initial conditions, topological transitivity , and ergodicity . Since such properties describe the main features required by real systems, the decision algorithms from our decidability results are then important tools for designing proper applications based on Additive CA. Indeed, we describe how our results can be exploited in some emblematic applications of cryptosystems , a paradigmatic and nowadays crucial applicative domain in which Additive CA are extensively used. We deal with methods for data encryption and, namely, we propose some strong modifications to the existing schemes in order to increase their security level and make attacks much harder.

Research paper thumbnail of On Symmetric Sandpiles

Lecture Notes in Computer Science, 2006

Research paper thumbnail of On Sand Automata

Lecture Notes in Computer Science, 2003

ABSTRACT In this paper we introduce sand automata in order to give a common and useful framework ... more ABSTRACT In this paper we introduce sand automata in order to give a common and useful framework for the study of most of the models of sandpiles. Moreover we give the possibility to have sources and sinks of “sand grains”. We prove a result which shows that the class of sand automata is rich enough to simulate any reasonable model of sandpiles based on local interaction rules. We also give an algorithm to find the fixed points of the evolutions of the sandpiles. Finally we prove that reversibility is equivalent to bijectivity.

Research paper thumbnail of Decidability of Sensitivity and Equicontinuity for Linear Higher-Order Cellular Automata

We study the dynamical behavior of linear higher-order cellular automata (HOCA) over \(\mathbb {Z... more We study the dynamical behavior of linear higher-order cellular automata (HOCA) over \(\mathbb {Z}_m\). In standard cellular automata the global state of the system at time t only depends on the state at time \(t-1\), while in HOCA it is a function of the states at time \(t-1\), ..., \(t-n\), where \(n\ge 1\) is the memory size. In particular, we provide easy-to-check necessary and sufficient conditions for a linear HOCA over \(\mathbb {Z}_m\) of memory size n to be sensitive to the initial conditions or equicontinuous. Our characterizations of sensitivity and equicontinuity extend the ones shown in [23] for linear cellular automata (LCA) over \(\mathbb {Z}_m^n\) in the case \(n=1\). We also prove that linear HOCA over \(\mathbb {Z}_m\) of memory size n are indistinguishable from a subclass of LCA over \(\mathbb {Z}_m^n\). This enables to decide injectivity and surjectivity for linear HOCA over \(\mathbb {Z}_m\) of memory size n by means of the decidable characterizations of injecti...

Research paper thumbnail of Rule Space Transformations and One-Dimensional Cellular Automata

Research paper thumbnail of On Sand Automata

Lecture Notes in Computer Science, 2003

ABSTRACT In this paper we introduce sand automata in order to give a common and useful framework ... more ABSTRACT In this paper we introduce sand automata in order to give a common and useful framework for the study of most of the models of sandpiles. Moreover we give the possibility to have sources and sinks of “sand grains”. We prove a result which shows that the class of sand automata is rich enough to simulate any reasonable model of sandpiles based on local interaction rules. We also give an algorithm to find the fixed points of the evolutions of the sandpiles. Finally we prove that reversibility is equivalent to bijectivity.

Research paper thumbnail of Non-uniform cellular automata: Classes, dynamics, and decidability

Information & Computation, Jun 1, 2012

Research paper thumbnail of An Easy to Check Characterization of Positive Expansivity for Additive Cellular Automata Over a Finite Abelian Group

Research paper thumbnail of Hard to Detect Factors of Univariate Integer Polynomials

Mathematics

We investigate the computational complexity of deciding whether a given univariate integer polyno... more We investigate the computational complexity of deciding whether a given univariate integer polynomial p(x) has a factor q(x) satisfying specific additional constraints. When the only constraint imposed on q(x) is to have a degree smaller than the degree of p(x) and greater than zero, the problem is equivalent to testing the irreducibility of p(x) and then it is solvable in polynomial time. We prove that deciding whether a given monic univariate integer polynomial has factors satisfying additional properties is NP-complete in the strong sense. In particular, given any constant value k∈Z, we prove that it is NP-complete in the strong sense to detect the existence of a factor that returns a prescribed value when evaluated at x=k (Theorem 1) or to detect the existence of a pair of factors—whose product is equal to the original polynomial—that return the same value when evaluated at x=k (Theorem 2). The list of all the properties we have investigated in this paper is reported at the end ...

Research paper thumbnail of Pure reaction automata

Natural computing, May 29, 2024

Research paper thumbnail of Computational Complexity of Rule Distributions of Non-uniform Cellular Automata

Research paper thumbnail of MDDs Boost Equation Solving on Discrete Dynamical Systems

Research paper thumbnail of Decidable Properties of 2D Cellular Automata

Lecture Notes in Computer Science, 2008

In this paper we study some decidable properties of two-dimensional cellular automata (2D CA). Th... more In this paper we study some decidable properties of two-dimensional cellular automata (2D CA). The notion of closingness is generalized to the 2D case and it is linked to permutivity and openness. The major contributions of this work are two deep constructions which ...

Research paper thumbnail of Solving Equations on Discrete Dynamical Systems (Extended version)

arXiv (Cornell University), Apr 30, 2019

Research paper thumbnail of Cellular Automata and Discrete Complex Systems

Research paper thumbnail of Chaotic Behavior of Cellular Automata

Springer eBooks, 2009

Université de Marne la Vallée.

Research paper thumbnail of An Efficient Algorithm Deciding Chaos for Linear Cellular Automata Over (Z/Mz)^N with Applications to Data Encryption

Research paper thumbnail of An Algorithmic Pipeline for Solving Equations over Discrete Dynamical Systems Modelling Hypothesis on Real Phenomena

arXiv (Cornell University), Nov 9, 2022

Research paper thumbnail of Basic Properties for Sand Automata

HAL (Le Centre pour la Communication Scientifique Directe), Sep 1, 2005

Research paper thumbnail of Foreword: asynchronous behavior of cellular automata and discrete models

Natural Computing, Oct 20, 2015

This special issue contains a selection of papers presented at the ‘‘Third International Workshop... more This special issue contains a selection of papers presented at the ‘‘Third International Workshop on Asynchronous Cellular Automata and Asynchronous Discrete Models’’ (ACA 2014), held as a satellite workshop of the 11th International Conference on Cellular Automata for Research and Industry (ACRI 2014) in Krakow (Poland) in September 2014. Six papers were selected and, after an additional review process, five of them have been included in this special issue. They are now presented in an extended and improved form with respect to the already refereed workshop version that appeared in the proceedings of the ACRI 2014 conference. The ACA workshop is devoted to the theme of asynchrony, a hot topic, inside Cellular Automata and other Discrete Models as, for instance, Boolean Networks. Cellular Automata are a well-known formal tool for modeling complex systems; they are considered in many scientific fields and industrial applications. Synchronicity is one of the main features of Cellular Automata evolutions. Indeed, in the most common Cellular Automata framework, all cells are updated simultaneously at each discrete time step by means of a same rule. Recent trends consider the modeling of asynchronous systems based on local and possibly non-uniform interactions. The aim of this workshop is to bring together researchers dealing with the theme of the asynchrony inside Cellular Automata and Discrete Models. Typical, but not exclusive, topics of the workshop are dynamics, complexity and computational issues, emergent properties, models of parallelism and distributed systems, and models of real phenomena. The paper ‘‘Local structure approximation as a predictor of second-order phase transitions in asynchronous cellular automata’’ by Henryk Fukś and Nazim Fates considers aasynchronous elementary cellular automata, that is elementary cellular automata in which each cell independently updates with probability a. By means of an extension of the mean-field approximation technique, the authors study the phase transitions in such automata, i.e., the changes of the dynamical behavior which may occur when the parameter a varies. In the paper ‘‘Supercritical probabilistic cellular automata: How effective is the synchronous updating?’’, PierreYves Louis deals with the issue of quantifying the effectiveness of the parallel updating in probabilistic cellular automata, i.e., cellular automata where the local rule is defined by means of a probability. Two interesting classes of probabilistic cellular automata are considered. An analysis of simulation is presented and shows that the behavior of these classes is nearly asynchronous when transition phase phenomena occur. Boolean Networks model the dynamical interaction of components which take a binary state. They have been & Alberto Dennunzio dennunzio@disco.unimib.it

Research paper thumbnail of Decidable characterizations of dynamical properties for additive cellular automata over a finite abelian group with applications to data encryption

Information Sciences, Jul 1, 2021

Abstract Additive cellular automata over a finite abelian group are a wide class of cellular auto... more Abstract Additive cellular automata over a finite abelian group are a wide class of cellular automata (CA) that are able to exhibit the complex behaviors of general CA and are often exploited for designing applications in different practical contexts. We provide decidable characterizations for Additive CA of the following important properties defining complex behaviors of complex systems: injectivity , surjectivity, equicontinuity, sensitivity to the initial conditions, topological transitivity , and ergodicity . Since such properties describe the main features required by real systems, the decision algorithms from our decidability results are then important tools for designing proper applications based on Additive CA. Indeed, we describe how our results can be exploited in some emblematic applications of cryptosystems , a paradigmatic and nowadays crucial applicative domain in which Additive CA are extensively used. We deal with methods for data encryption and, namely, we propose some strong modifications to the existing schemes in order to increase their security level and make attacks much harder.

Research paper thumbnail of On Symmetric Sandpiles

Lecture Notes in Computer Science, 2006

Research paper thumbnail of On Sand Automata

Lecture Notes in Computer Science, 2003

ABSTRACT In this paper we introduce sand automata in order to give a common and useful framework ... more ABSTRACT In this paper we introduce sand automata in order to give a common and useful framework for the study of most of the models of sandpiles. Moreover we give the possibility to have sources and sinks of “sand grains”. We prove a result which shows that the class of sand automata is rich enough to simulate any reasonable model of sandpiles based on local interaction rules. We also give an algorithm to find the fixed points of the evolutions of the sandpiles. Finally we prove that reversibility is equivalent to bijectivity.

Research paper thumbnail of Decidability of Sensitivity and Equicontinuity for Linear Higher-Order Cellular Automata

We study the dynamical behavior of linear higher-order cellular automata (HOCA) over \(\mathbb {Z... more We study the dynamical behavior of linear higher-order cellular automata (HOCA) over \(\mathbb {Z}_m\). In standard cellular automata the global state of the system at time t only depends on the state at time \(t-1\), while in HOCA it is a function of the states at time \(t-1\), ..., \(t-n\), where \(n\ge 1\) is the memory size. In particular, we provide easy-to-check necessary and sufficient conditions for a linear HOCA over \(\mathbb {Z}_m\) of memory size n to be sensitive to the initial conditions or equicontinuous. Our characterizations of sensitivity and equicontinuity extend the ones shown in [23] for linear cellular automata (LCA) over \(\mathbb {Z}_m^n\) in the case \(n=1\). We also prove that linear HOCA over \(\mathbb {Z}_m\) of memory size n are indistinguishable from a subclass of LCA over \(\mathbb {Z}_m^n\). This enables to decide injectivity and surjectivity for linear HOCA over \(\mathbb {Z}_m\) of memory size n by means of the decidable characterizations of injecti...

Research paper thumbnail of Rule Space Transformations and One-Dimensional Cellular Automata

Research paper thumbnail of On Sand Automata

Lecture Notes in Computer Science, 2003

ABSTRACT In this paper we introduce sand automata in order to give a common and useful framework ... more ABSTRACT In this paper we introduce sand automata in order to give a common and useful framework for the study of most of the models of sandpiles. Moreover we give the possibility to have sources and sinks of “sand grains”. We prove a result which shows that the class of sand automata is rich enough to simulate any reasonable model of sandpiles based on local interaction rules. We also give an algorithm to find the fixed points of the evolutions of the sandpiles. Finally we prove that reversibility is equivalent to bijectivity.

Research paper thumbnail of Non-uniform cellular automata: Classes, dynamics, and decidability

Information & Computation, Jun 1, 2012

Research paper thumbnail of An Easy to Check Characterization of Positive Expansivity for Additive Cellular Automata Over a Finite Abelian Group

Research paper thumbnail of Hard to Detect Factors of Univariate Integer Polynomials

Mathematics

We investigate the computational complexity of deciding whether a given univariate integer polyno... more We investigate the computational complexity of deciding whether a given univariate integer polynomial p(x) has a factor q(x) satisfying specific additional constraints. When the only constraint imposed on q(x) is to have a degree smaller than the degree of p(x) and greater than zero, the problem is equivalent to testing the irreducibility of p(x) and then it is solvable in polynomial time. We prove that deciding whether a given monic univariate integer polynomial has factors satisfying additional properties is NP-complete in the strong sense. In particular, given any constant value k∈Z, we prove that it is NP-complete in the strong sense to detect the existence of a factor that returns a prescribed value when evaluated at x=k (Theorem 1) or to detect the existence of a pair of factors—whose product is equal to the original polynomial—that return the same value when evaluated at x=k (Theorem 2). The list of all the properties we have investigated in this paper is reported at the end ...