87 research outputs found
A compact topology for sand automata
In this paper, we exhibit a strong relation between the sand automata
configuration space and the cellular automata configuration space. This
relation induces a compact topology for sand automata, and a new context in
which sand automata are homeomorphic to cellular automata acting on a specific
subshift. We show that the existing topological results for sand automata,
including the Hedlund-like representation theorem, still hold. In this context,
we give a characterization of the cellular automata which are sand automata,
and study some dynamical behaviors such as equicontinuity. Furthermore, we deal
with the nilpotency. We show that the classical definition is not meaningful
for sand automata. Then, we introduce a suitable new notion of nilpotency for
sand automata. Finally, we prove that this simple dynamical behavior is
undecidable
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
Foreword: cellular automata and applications
International audienceThis special issue contains four papers presented during theworkshop, ââ18th International Workshop on CellularAutomata and Discrete Complex Systemsââ (Automata2012), held in La Marana, Corsica island (France) in theperiod September 19â21th, 2012.The aim of this workshop is to establish and maintain apermanent, international, multidisciplinary forum for thecollaboration of researchers in the field of Cellular Automata(CA) and Discrete Complex Systems (DCS), providea platform for presenting and discussing new ideas andresults, and support the development of theory and applicationsof CA and DCS.Typical, but not exclusive, topics of the workshop are:dynamics aspects, algorithmic, computational and complexityissues, emergent properties, formal language processing,models of parallelism and distributed systems,phenomenological descriptions, scientific modeling andpractical applications.After an additional review process, four papers wereselected and included in this special issue. They are nowpresented in an extended and improved form with respectto the already refereed workshop version that appeared inthe proceedings of Automata 2012.The paper ââComputation of Functions on n Bits byAsynchronous Clocking Cellular Automataââ by MichaelVielhaber aims at proving that different functions on binaryvectors can be computed by changing the updating schemefrom a fully synchronous to an asynchronous one on somefixed CA local rule.In their paper ââSolving the Parity Problem in OneâDimensional Cellular Automataââ, Heather Betel, PedroP. B. de Oliveira, and Paola Flocchini deal with the parityproblem in oneâdimensional cellular automata (CA): a CAlocal rule solves the parity problem if, starting from anyinitial configuration, the CA converges to the 0âconfiguration(resp., the 1âconfiguration) if and only if the initialconfiguration contains an even number of 1s (resp., an oddnumber of 1s). In particular, authors focus on the neighborhoodsize of CA rules solving the problem.Murillo G. Carneiro and Gina M. B. Oliveira present inthe paper ââSynchronous Cellular Automata-Based Schedulerinitialized by Heuristic and modeled by a Pseudolinearneighborhoodââ two approaches based on CA to thetask scheduling problem in multiprocessor systems.The implementation of cellular automata on processorarrays is considered by Jean-Vivien Millo and Robertde Simone in the paper ââExplicit routing schemes forimplementation of cellular automata on processor arraysââ.They deal with the trade-offs between the generality of theCA neighborhood and the limited expressive power providedby physical platforms. This is an extremely hot topicwhich will help in turning CA towards real extendedapplications.We would like to warmly thank the authors for theirwork and effort which made this special issue possible.Special thanks go to all referees for their valuable contributionsboth during the selection and the final reviewprocess. Finally, we also want to thank Professor GrzegorzRozenberg for offering us the opportunity to publish thisspecial issue in Natural Computing
An Easily Checkable Algebraic Characterization of Positive Expansivity for Additive Cellular Automata over a Finite Abelian Group
We provide an easily checkable algebraic characterization of positive
expansivity for Additive Cellular Automata over a finite abelian group. First
of all, an easily checkable characterization of positive expansivity is
provided for the non trivial subclass of Linear Cellular Automata over the
alphabet . Then, we show how it can be exploited to decide positive
expansivity for the whole class of Additive Cellular Automata over a finite
abelian group.Comment: 12 page
A compact topology for sand automata
In this paper, we exhibit a strong relation between the sand automata configuration space and the cellular automata configuration space. This relation induces a compact topology for sand automata, and a new context in which sand automata are homeomorphic to cellular automata acting on a specific subshift. We show that the existing topological results for sand automata, including the Hedlund-like representation theorem, still hold. In this context, we give a characterization of the cellular automata which are sand automata, and study some dynamical behaviors such as equicontinuity. Furthermore, we deal with the nilpotency. We show that the classical definition is not meaningful for sand automata. Then, we introduce a suitable new notion of nilpotency for sand automata. Finally, we prove that this simple dynamical behavior is undecidable
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.Comment: Paper submitted to an international journal on June 9, 2011. This is
an extended and improved version of the conference paper: G. Cattaneo, A.
Dennunzio, E. Formenti, and J. Provillard. "Non-uniform cellular automata".
In Proceedings of LATA 2009, volume 5457 of Lecture Notes in Computer
Science, pages 302-313. Springe
An Easy to Check Characterization of Positive Expansivity for Additive Cellular Automata over a Finite Abelian Group
Additive cellular automata over a finite abelian group are a wide class of cellular automata (CA) that are able to exhibit most of the complex behaviors of general CA and they are often exploited for designing applications in different practical contexts. We provide an easy to check algebraic characterization of positive expansivity for Additive Cellular Automata over a finite abelian group. We stress that positive expansivity is an important property that defines a condition of strong chaos for CA and, for this reason, an easy to check characterization of positive expansivity turns out to be crucial for designing proper applications based on Additive CA and where a condition of strong chaos is required. First of all, in the paper an easy to check algebraic characterization of positive expansivity is provided for the non trivial subclass of Linear Cellular Automata over the alphabet (Z/mZ)n . Then, we show how it can be exploited to decide positive expansivity for the whole class of Additive Cellular Automata over a finite abelian group
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