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Enrico Formenti

Publications and source records attributed to Enrico Formenti.

33 records · Page 2Linked to original sources
arXiv2019

Complexity of the dynamics of reaction systems

Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena that complements the more traditional approaches, for instance those based on differential equations. A comprehensive list of decision problems about the dynamical behavior of reaction systems (such as cycles and fixed/periodic points, attractors, and reachability) is provided along with the corresponding computational complexity, which ranges from tractable problems to PSPACE-complete problems.

cs.FL↗
arXiv2019

On the dynamical behaviour of linear higher-order cellular automata and its decidability

Higher-order cellular automata (HOCA) are a variant of cellular automata (CA) used in many applications (ranging, for instance, from the design of secret sharing schemes to data compression and image processing), and in which the global state of the system at time $t$ depends not only on the state at time $t-1$, as in the original model, but also on the states at time $t-2, \ldots, t-n$, where $n$ is the memory size of the HOCA. We provide decidable characterizations of two important dynamical properties, namely, sensitivity to the initial conditions and equicontinuity, for linear HOCA over the alphabet $\mathbb{Z}_m$. Such characterizations extend the ones shown in [23] for linear CA (LCA) over the alphabet $\mathbb{Z}^{n}_m$ in the case $n=1$. We also prove that linear HOCA of size memory $n$ over $\mathbb{Z}_m$ form a class that is indistinguishable from a specific subclass of LCA over $\mathbb{Z}_m^n$. This enables to decide injectivity and surjectivity for linear HOCA of size memory $n$ over $\mathbb{Z}_m$ using the decidable characterization provided in [2] and [19] for injectivity and surjectivity of LCA over $\mathbb{Z}^n_m$. Finally, we prove an equivalence between LCA over $\mathbb{Z}_m^n$ and an important class of non-uniform CA, another variant of CA used in many applications.

cs.FL↗
arXiv2018

Computational complexity of the avalanche problem on one dimensional Kadanoff sandpiles

In this paper we prove that the general avalanche problem AP is in NC, for the Kadanoff sandpile model in one dimension, answering an open problem of Formenti, Goles and Martin in 2010. Thus adding one more item to the (slowly) growing list of dimension sensitive problems since in higher dimensions the problem is P-complete (for monotone sandpiles).

cs.CC↗
arXiv2016

Constructing Orthogonal Latin Squares from Linear Cellular Automata

We undertake an investigation of combinatorial designs engendered by cellular automata (CA), focusing in particular on orthogonal Latin squares and orthogonal arrays. The motivation is of cryptographic nature. Indeed, we consider the problem of employing CA to define threshold secret sharing schemes via orthogonal Latin squares. We first show how to generate Latin squares through bipermutive CA. Then, using a characterization based on Sylvester matrices, we prove that two linear CA induce a pair of orthogonal Latin squares if and only if the polynomials associated to their local rules are relatively prime.

cs.DM↗
arXiv2013

Acceptance conditions for omega-languages and the Borel hierarchy

This paper investigates acceptance conditions for finite automata recognizing omega-regular languages. As a first result, we show that, under any acceptance condition that can be defined in the MSO logic, a finite automaton can recognize at most omega-regular languages. Starting from this, the paper aims at classifying acceptance conditions according to their expressive power and at finding the exact position of the classes of omega-languages they induced according to the Borel hierarchy. A new interesting acceptance condition is introduced and fully characterized. A step forward is also made in the understanding of the expressive power of (fin, =).

cs.FL↗
arXiv2012

Proceedings 18th international workshop on Cellular Automata and Discrete Complex Systems and 3rd international symposium Journées Automates Cellulaires

This volume contains the proceedings of the 18th International workshop AUTOMATA and the 3rd international symposium JAC. AUTOMATA workshop series aims at gathering researchers from all over the world working in fundamental aspects of cellular automata and related discrete complex systems. Topics cover (although they are not limited to): dynamics, topological, ergodic and algebraic aspects, algorithmic and complexity issues, emergent properties, formal language processing, symbolic dynamics, models of parallelism and distributed systems, phenomenological descriptions, scientific modeling and practical applications. JAC (Journées Automates Cellulaires) is a bi-annual symposium covering the same topics and was created to have a very high standard international conference in the domain. This one will be the third event of the series after Uzès (2008, France), Turku (2010, Finland).

cs.FL↗
arXiv2011

Non-uniform cellular automata and distributions of rules

In this paper we study $ν$-CA on one-dimensional lattice defined over a finite set of local rules. The main goal is to determine how the local rules can be mixed to ensure the produced $ν$-CA has some properties. In a first part, we give some background for the study of $ν$-CA. Then surjectivity and injectivity are studied using a variant of DeBruijn graphs. The next part is dedicated to the number-conserving property.

cs.FL↗
arXiv2011

Non-Uniform Cellular Automata: classes, dynamics, and decidability

The dynamical behavior of non-uniform cellular automata is compared with the one of classical cellular automata. Several differences and similarities are pointed out by a series of examples. Decidability of basic properties like surjectivity and injectivity is also established. The final part studies a strong form of equicontinuity property specially suited for non-uniform cellular automata.

cs.FL↗
arXiv2011

Computational Aspects of Asynchronous CA

This work studies some aspects of the computational power of fully asynchronous cellular automata (ACA). We deal with some notions of simulation between ACA and Turing Machines. In particular, we characterize the updating sequences specifying which are "universal", i.e., allowing a (specific family of) ACA to simulate any TM on any input. We also consider the computational cost of such simulations.

cs.FL↗
arXiv2011

Ultimate Traces of Cellular Automata

A cellular automaton (CA) is a parallel synchronous computing model, which consists in a juxtaposition of finite automata (cells) whose state evolves according to that of their neighbors. Its trace is the set of infinite words representing the sequence of states taken by some particular cell. In this paper we study the ultimate trace of CA and partial CA (a CA restricted to a particular subshift). The ultimate trace is the trace observed after a long time run of the CA. We give sufficient conditions for a set of infinite words to be the trace of some CA and prove the undecidability of all properties over traces that are stable by ultimate coincidence.

cs.FL↗
arXiv2009

2D cellular automata: dynamics and undecidability

In this paper we introduce the notion of quasi-expansivity for 2D CA and we show that it shares many properties with expansivity (that holds only for 1D CA). Similarly, we introduce the notions of quasi-sensitivity and prove that the classical dichotomy theorem holds in this new setting. Moreover, we show a tight relation between closingness and openness for 2D CA. Finally, the undecidability of closingness property for 2D CA is proved.

cs.FL↗
arXiv2007

Sofic Trace of a Cellular Automaton

The trace subshift of a cellular automaton is the subshift of all possible columns that may appear in a space-time diagram, ie the infinite sequence of states of a particular cell of a configuration; in the language of symbolic dynamics one says that it is a factor system. In this paper we study conditions for a sofic subshift to be the trace of a cellular automaton.

math.DS↗
arXiv2006

On symmetric sandpiles

A symmetric version of the well-known SPM model for sandpiles is introduced. We prove that the new model has fixed point dynamics. Although there might be several fixed points, a precise description of the fixed points is given. Moreover, we provide a simple closed formula for counting the number of fixed points originated by initial conditions made of a single column of grains.

cs.CC↗
arXiv2004

Basic properties for sand automata

We prove several results about the relations between injectivity and surjectivity for sand automata. Moreover, we begin the exploration of the dynamical behavior of sand automata proving that the property of nilpotency is undecidable. We believe that the proof technique used for this last result might reveal useful for many other results in this context.

cs.CC↗