On generative morphological diversity of elementary cellular automata

Purpose: Studies in complexity of cellular automata do usually deal with measures taken on integral dynamics or statistical measures of space-time configurations. No one has tried to analyze a generative power of cellular-automaton machines. The purpose of this paper is to fill the gap and develop a basis for future studies in generative complexity of large-scale spatially extended systems. Design/methodology/approach: Let all but one cell be in alike state in initial configuration of a one-dimensional cellular automaton. A generative morphological diversity of the cellular automaton is a number of different three-by-three cell blocks occurred in the automaton's space-time configuration. Findings: The paper builds a hierarchy of generative diversity of one-dimensional cellular automata with binary cell-states and ternary neighborhoods, discusses necessary conditions for a cell-state transition rule to be on top of the hierarchy, and studies stability of the hierarchy to initial conditions. Research limitations/implications: The method developed will be used - in conjunction with other complexity measures - to built a complete complexity maps of one- and two-dimensional cellular automata, and to select and breed local transition functions with highest degree of generative morphological complexity. Originality/value: The hierarchy built presents the first ever approach to formally characterize generative potential of cellular automata. © Emerald Group Publishing Limited

Combinatorics on Words 10th International Conference

This volume contains the Local Proceedings of the Tenth International Conference on WORDS, that took place at the Kiel University, Germany, from the 14th to the 17th September 2015. WORDS is the main conference series devoted to the mathematical theory of words, and it takes place every two years. The first conference in the series was organised in 1997 in Rouen, France, with the following editions taking place in Rouen, Palermo,Turku, Montreal, Marseille, Salerno, Prague, and Turku. The main object in the scope of the conference, words, are finite or infinite sequences of symbols over a finite alphabet. They appear as natural and basic mathematical model in many areas, theoretical or applicative. Accordingly, the WORDS conference is open to both theoretical contributions related to combinatorial, algebraic, and algorithmic aspects of words, as well as to contributions presenting application of the theory of words, for instance, in other fields of computer science, inguistics, biology and bioinformatics, or physics. For the second time in the history of WORDS, after the 2013 edition, a refereed proceedings volume was published in Springer’s Lecture Notes in Computer Science series. In addition, this local proceedings volume was published in the Kiel Computer Science Series of the Kiel University. Being a conference at the border between theoretical computer science and mathematics, WORDS tries to capture in its two proceedings volumes the characteristics of the conferences from both these worlds. While the Lecture Notes in Computer Science volume was dedicated to formal contributions, this local proceedings volume allows, in the spirit of mathematics conferences, the publication of several contributions informing on current research and work in progress in areas closely connected to the core topics of WORDS. All the papers, the ones published in the Lecture Notes in Computer Science proceedings volume or the ones from this volume, were refereed to high standards by the members of the Program Committee. Following the conference, a special issue of the Theoretical Computer Science journal will be edited, containing extended versions of papers from both proceedings volumes. In total, the conference hosted 18 contributed talks. The papers on which 14 of these talks were based, were published in th LNCS volume; the other 4 are published in this volume. In addition to the contributed talks, the conference program included six invited talks given by leading experts in the areas covered by the WORDS conference: Jörg Endrullis (Amsterdam), Markus Lohrey (Siegen), Jean Néraud (Rouen), Dominique Perrin (Paris), Michaël Rao (Lyon), Thomas Stoll (Nancy). WORDS 2015 was the tenth conference in the series, so we were extremely happy to welcome, as invited speaker at this anniversary edition, Jean Néraud, one of the initiators of the series and the main organiser of the first two editions of this conference. We thank all the invited speakers and all the authors of submitted papers for their contributions to the the success of the conference. We are grateful to the members of the Program Committee for their work that lead to the selection of the contributed talks, and, implicitly, of the papers published in this volume. They were assisted in their task by a series of external referees, gratefully acknowledged below. The submission and reviewing process used the Easychair system; we thank Andrej Voronkov for this system which facilitated the work of the Programme Committee and the editors considerably. We grateful thank Gheorghe Iosif for designing the logo, poster, and banner of WORDS 2015; the logo of the conference can be seen on the front cover of this book. We also thank the editors of the Kiel Computer Science Series, especially Lasse Kliemann, for their support in editing this volume. Finally, we thank the Organising Committee of WORDS 2015 for ensuring the smooth run of the conference

STATE-OF-ART Algorithms for Injectivity and Bounded Surjectivity of One-dimensional Cellular Automata

Surjectivity and injectivity are the most fundamental problems in cellular automata (CA). We simplify and modify Amoroso's algorithm into optimum and make it compatible with fixed, periodic and reflective boundaries. A new algorithm (injectivity tree algorithm) for injectivity is also proposed. After our theoretic analysis and experiments, our algorithm for injectivity can save much space and 90\% or even more time compared with Amoroso's algorithm for injectivity so that it can support the decision of CA with larger neighborhood sizes. At last, we prove that the reversibility with the periodic boundary and global injectivity of one-dimensional CA is equivalent

Cellular Automata

Modelling and simulation are disciplines of major importance for science and engineering. There is no science without models, and simulation has nowadays become a very useful tool, sometimes unavoidable, for development of both science and engineering. The main attractive feature of cellular automata is that, in spite of their conceptual simplicity which allows an easiness of implementation for computer simulation, as a detailed and complete mathematical analysis in principle, they are able to exhibit a wide variety of amazingly complex behaviour. This feature of cellular automata has attracted the researchers' attention from a wide variety of divergent fields of the exact disciplines of science and engineering, but also of the social sciences, and sometimes beyond. The collective complex behaviour of numerous systems, which emerge from the interaction of a multitude of simple individuals, is being conveniently modelled and simulated with cellular automata for very different purposes. In this book, a number of innovative applications of cellular automata models in the fields of Quantum Computing, Materials Science, Cryptography and Coding, and Robotics and Image Processing are presented

Use of cellular automata-based methods for understanding material-process-microstructure relations in alloy-based additive processes

Deposition of metals through additive manufacturing has garnered research interest as of late due to the large range of potential industry applications. In particular, direct metal deposition processes such as Laser Engineered Net Shaping (LENS) have the ability to construct near net shape parts, open cellular structures, compositionally graded parts, and parts with improved mechanical properties over those manufactured via traditional methods such as casting and forging. To utilize additive processes to their full potential, it is imperative that the relationships among process parameters, development of the molten pool, microstructure, and properties are understood. Our goal in applying computational modeling to this problem is to aid in our understanding of such relationships to guide future experiments towards sets of alloying additions and deposition conditions that produce preferred microstructures. Cellular Automata (CA) based modeling techniques provide a way to bridge the scales of the complex phenomena that occur during AM processes, reducing them to physics-based rules for the evolution of cell state variables; in particular, this makes these methods well-suited for large scale parallel computing problems and large ensembles of simulations. CA is applied at the scale of individual dendrites yielding quantitative agreement with analytical models for dendrite tip undercooling as a function of solidification velocity. For dendritic colonies, CA modeled microstructures yielded favorable quantitative and qualitative agreement with expected trends in primary arm spacing, side branching, solute segregation, and non-equilibrium growth phenomena such as solute trapping and banded growth morphology. CA is also applied at the scale of multiple grains to investigate the columnar to equiaxed transition in 2D and 3D with varied nucleation undercooling, alloying addition, and interfacial response function. The lattice Boltzmann (LB) method for fluid transport is combined with COMSOL Multiphysics simulations of melt pool dynamics and the dendrite-scale CA for coupled simulation of fluid flow, solute transport, and solidification, yielding good agreement on microsegregation and dendrite arm spacing with experimental results for LENS alloy deposition. A thermal lattice Boltzmann (TLB) model of the melt pool is also developed and combined with the grain-scale CA for parallel, concurrent multiscale simulation of fluid flow, heat transport, and grain growth for LENS-representative conditions, showcasing the model\u27s ability to predict microstructure trends with changes in process conditions or alloying additions. The ability of CA to accurately predict many aspects of and trends regarding alloy solidification in additive processes show a promising future for using similar codes to augment experimental results for new alloy development, while the parallelizability and computational efficiency of CA show its potential for use in Exascale computing application codes