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, ‘‘18th International Workshop on CellularAutomata and Discrete Complex Systems’’ (Automata2012), held in La Marana, Corsica island (France) in theperiod September 19–21th, 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 ‘‘Computation of Functions on n Bits byAsynchronous Clocking Cellular Automata’’ 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 ‘‘Solving the Parity Problem in One–Dimensional Cellular Automata’’, Heather Betel, PedroP. B. de Oliveira, and Paola Flocchini deal with the parityproblem in one–dimensional cellular automata (CA): a CAlocal rule solves the parity problem if, starting from anyinitial configuration, the CA converges to the 0–configuration(resp., the 1–configuration) 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 ‘‘Synchronous Cellular Automata-Based Schedulerinitialized by Heuristic and modeled by a Pseudolinearneighborhood’’ 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 ‘‘Explicit routing schemes forimplementation of cellular automata on processor arrays’’.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 $(\Z/m\Z)^n$. 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.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