Revisiting the Rice Theorem of Cellular Automata

A cellular automaton is a parallel synchronous computing model, which consists in a juxtaposition of finite automata whose state evolves according to that of their neighbors. It induces a dynamical system on the set of configurations, i.e. the infinite sequences of cell states. The limit set of the cellular automaton is the set of configurations which can be reached arbitrarily late in the evolution. In this paper, we prove that all properties of limit sets of cellular automata with binary-state cells are undecidable, except surjectivity. This is a refinement of the classical "Rice Theorem" that Kari proved on cellular automata with arbitrary state sets.Comment: 12 pages conference STACS'1

Four states are enough!

International audienceThis paper presents a 1D intrinsically universal cellular automaton with four states for a first neighbors neighborhood, improving on the previous lower bound and getting nearer to the Turing universality bound. Intrinsic universality is discussed. Construction and proof rely on a combination of bulking techniques with programming using particles and collisions

Collisions and their Catenations: Ultimately Periodic Tilings of the Plane

Motivated by the study of cellular automata algorithmics and dynamics, we investigate an extension of ultimately periodic words to two-dimensional infinite words: collisions. A natural composition operation on tilings leads to a catenation operation on collisions. By existence of aperiodic tile sets, ultimately periodic tilings of the plane cannot generate all possible tilings but exhibit some useful properties of their one-dimensional counterparts: ultimately periodic tilings are recursive, very regular, and tiling constraints are easy to preserve by catenation. We show that, for a given catenation scheme of finitely many collisions, the generated set of collisions is semi-linear

Descriptive complexity for pictures languages (extended abstract)

This paper deals with descriptive complexity of picture languages of any dimension by syntactical fragments of existential second-order logic. - We uniformly generalize to any dimension the characterization by Giammarresi et al. \cite{GRST96} of the class of \emph{recognizable} picture languages in existential monadic second-order logic. - We state several logical characterizations of the class of picture languages recognized in linear time on nondeterministic cellular automata of any dimension. They are the first machine-independent characterizations of complexity classes of cellular automata. Our characterizations are essentially deduced from normalization results we prove for first-order and existential second-order logics over pictures. They are obtained in a general and uniform framework that allows to extend them to other "regular" structures. Finally, we describe some hierarchy results that show the optimality of our logical characterizations and delineate their limits.Comment: 33 pages - Submited to Lics 201

A Particular Universal Cellular Automaton

Signals are a classical tool used in cellular automata constructions that proved to be useful for language recognition or firing-squad synchronisation. Particles and collisions formalize this idea one step further, describing regular nets of colliding signals. In the present paper, we investigate the use of particles and collisions for constructions involving an infinite number of interacting particles. We obtain a high-level construction for a new smallest intrinsically universal cellular automaton with 4 states

The Protist Ribosomal Reference database (PR2): a catalog of unicellular eukaryote Small Sub-Unit rRNA sequences with curated taxonomy

The interrogation of genetic markers in environmental meta-barcoding studies is currently seriously hindered by the lack of taxonomically curated reference data sets for the targeted genes. The Protist Ribosomal Reference database (PR2, http://ssu-rrna.org/) provides a unique access to eukaryotic small sub-unit (SSU) ribosomal RNA and DNA sequences, with curated taxonomy. The database mainly consists of nuclear-encoded protistan sequences. However, metazoans, land plants, macrosporic fungi and eukaryotic organelles (mitochondrion, plastid and others) are also included because they are useful for the analysis of high-troughput sequencing data sets. Introns and putative chimeric sequences have been also carefully checked. Taxonomic assignation of sequences consists of eight unique taxonomic fields. In total, 136 866 sequences are nuclear encoded, 45 708 (36 501 mitochondrial and 9657 chloroplastic) are from organelles, the remaining being putative chimeric sequences. The website allows the users to download sequences from the entire and partial databases (including representative sequences after clustering at a given level of similarity). Different web tools also allow searches by sequence similarity. The presence of both rRNA and rDNA sequences, taking into account introns (crucial for eukaryotic sequences), a normalized eight terms ranked-taxonomy and updates of new GenBank releases were made possible by a long-term collaboration between experts in taxonomy and computer scientist

Gene family expansions and contractions are associated with host range in plant pathogens of the genus Colletotrichum

Background: Many species belonging to the genus Colletotrichum cause anthracnose disease on a wide range of plant species. In addition to their economic impact, the genus Colletotrichum is a useful model for the study of the evolution of host specificity, speciation and reproductive behaviors. Genome projects of Colletotrichum species have already opened a new era for studying the evolution of pathogenesis in fungi. Results: We sequenced and annotated the genomes of four strains in the Colletotrichum acutatum species complex (CAsc), a clade of broad host range pathogens within the genus. The four CAsc proteomes and secretomes along with those representing an additional 13 species (six Colletotrichum spp. and seven other Sordariomycetes) were classified into protein families using a variety of tools. Hierarchical clustering of gene family and functional domain assignments, and phylogenetic analyses revealed lineage specific losses of carbohydrate-active enzymes (CAZymes) and proteases encoding genes in Colletotrichum species that have narrow host range as well as duplications of these families in the CAsc. We also found a lineage specific expansion of necrosis and ethylene-inducing peptide 1 (Nep1)-like protein (NLPs) families within the CAsc. Conclusions: This study illustrates the plasticity of Colletotrichum genomes, and shows that major changes in host range are associated with relatively recent changes in gene content

Rule 110: universality and catenations

ISBN 978-5-94057-377-7International audienceCellular automata are a simple model of parallel computation. Many people wonder about the computing power of such a model. Following an idea of S. Wolfram [16], M. Cook [3] has proved than even one of the simplest cellular automata can embed any Turing computation. In this paper, we give a new high-level version of this proof using particles and collisions as introduced in [10]

Filling Curves Constructed in Cellular Automata with Aperiodic Tiling

Part 2: Regular PapersInternational audienceIn many constructions on cellular automata, information is transmitted with signals propagating through a defined background. In this paper, we investigate the possibility of using aperiodic tiling inside zones delimited by signals. More precisely, we study curves delineated by CA-constructible functions and prove that most of them can be filled with the NW-deterministic tile set defined by Kari [1]. The achieved results also hint a new possible way to study deterministic tile sets