Abstract. We study herewith the simple threshold cellular automata (CA), as perhaps the simplest broad class of CA with non-additive (i.e., non-linear and non-affine) local update rules. We characterize all possible computations of the most interesting rule for such CA, namely, the Majority (MAJ) rule, both in the classical, parallel CA case, and in case of the corresponding sequential CA where the nodes update sequentially, one at a time. We compare and contrast the configuration spaces of arbitrary simple threshold automata in those two cases, and point out that some parallel threshold CA cannot be simulated by any of their sequential counterparts. We show that the temporal cycles exist only in case of (some) parallel simple threshold CA, but can never take place in sequential threshold CA. We also show that most threshold CA have very few fixed point configurations and few (if any) cycle configurations, and that, while the MAJ sequential and parallel CA may have many fixed points, nonetheless “almost all” configurations, in both parallel and sequential cases, are transient states. 1

This tutorial provides a nonlinear dynamics perspective to Wolfram’s monumental work on A New Kind of Science. By mapping a Boolean local Rule, ortruth table, ontothepoint attractors of a specially tailored nonlinear dynamical system, we show how some of Wolfram’s empirical observations can be justified on firm ground. The advantage of this new approach for studying Cellular Automata phenomena is that it is based on concepts from nonlinear dynamics and attractors where many fuzzy concepts introduced by Wolfram via brute force observations can be defined and justified via mathematical analysis. The main result of Part I is the introduction of a fundamental concept called linear separability and a complexity index κ for each local Rule which characterizes the intrinsic geometrical structure of an induced “Boolean cube ” in three-dimensional Euclidean space. In particular, Wolfram’s seductive idea of a “threshold of

Intelligent nanomechanical devices that operate in an autonomous fashion are of great theoretical and practical interest. Recent successes in building large scale DNA nanostructures, in constructing DNA mechanical devices, and in DNA computing provide a solid foundation for the next step forward: designing autonomous DNA mechanical devices capable of arbitrarily complex behavior. One prototype system towards this goal can be a DNA mechanical device that is capable of universal computation, by mimicking the operation of a universal Turing machine. Building on our prior theoretical designs and a prototype experimental construction of autonomous unidirectional DNA walking devices that move along linear tracks, we present in this paper the design of a nanomechanical DNA device that autonomously mimics the operation of a 2-state 5color universal Turing machine. Our autonomous nanomechanical device, which we call an Autonomous DNA Turing Machine, is thus capable of universal computation and hence complex translational motion which we define as universal translational motion.

Bottom-up fabrication of nanoscale structures relies on chemical processes to direct self-assembly. The complexity, precision, and yield achievable by a one-pot reaction are limited by our ability to encode assembly instructions into the molecules themselves. Nucleic acids provide a platform for investigating these issues, as molecular structure and intramolecular interactions can encode growth rules. Here, we use DNA tiles and DNA origami to grow crystals containing a cellular automaton pattern. In a one-pot annealing reaction, 250 DNA strands first assemble into a set of 10 free tile types and a seed structure, then the free tiles grow algorithmically from the seed according to the automaton rules. In our experiments, crystals grew to ∼300 nm long, containing ∼300 tiles with an initial assembly error rate of ∼1.4 % per tile. This work provides evidence that programmable molecular self-assembly may be sufficient to create a wide range of complex objects in one-pot reactions. The WatsonsCrick complementarity of DNA molecules allows one to design not only simple double-stranded helices but also complicated woven structures consisting of many DNA strands. 1 Well-designed structures will self-assemble during annealing from a high initial temperature at which point all molecules are single-stranded to a lower final

Abstract. We give small universal Turing machines with state-symbol pairs of (6, 2), (3,3) and (2,4). These machines are weakly universal, which means that they have an infinitely repeated word to the left of their input and another to the right. They simulate Rule 110 and are currently the smallest known weakly universal Turing machines. Despite their small size these machines are efficient polynomial time simulators of Turing machines. 1

This report summarizes ten levels of abstraction that together span the continuum from the most elementary to the most general levels when modeling biological systems. It is shown how the neocybernetic principles can be seen as the key to reaching a holistic view of complex processes in general. Preface Concrete examples help to understand complex systems. In this report, the key point is to illustrate the basic mechanisms and properties of neocybernetic system models. Good visualizations are certainly needed. It is biological systems, or living systems, that are perhaps the most characteristic examples of cybernetic systems. This intuition is extended here to natural systems in general — indeed, it is all other than man-made ones that seem to be cybernetic. The word “biological ” in the title should be interpreted as “bio-logical ” — referring to general studies of any living systems, independent of the phenosphere. Starting from the concrete examples, connections to more abstract systems are found, and the discussions become more and more all-embracing in this text. However, the neocybernetic model framework still makes it possible to conceptually master the complexity. There is more information about neocybernetics available in Internet — also this report is available there in electronic form:

When constructing multiagent systems, the designer may approach the system as a collection of individuals or may view the entire system as a whole. In addition to these approaches, it may be beneficial to consider the interactions between the individuals and the whole. Borrowing ideas from the notion of social construction and building on previous work in synthetic social construction, this paper presents a framework wherein autonomous agents engage in a dialectic relationship with the society of agents around them. In this framework, agents recognize patterns of social activity in their societies, group such patterns into institutions, and form computational representations of those institutions. The paper presents a design framework describing this method of institutionalization, some implementation suggestions, and a discussion of possible applications.

Abstract. Reactive multiagent systems are shown to coevolve with explicit communication and cooperative behavior to solve lattice formation tasks. Comparable agents that lack the ability to communicate and cooperate are shown to be unsuccessful in solving the same tasks. The agents without any centralized supervision develop a communication protocol with a mutually agreed upon signaling scheme to share sensor data between a pair of individuals. The control system for these agents consists of identical cellular automata handling communication, cooperation and motion subsystems. Shannon’s entropy function was used as a fitness evaluator to evolve the desired cellular automata. The results are derived from computer simulations. 1

Complex systems theory promises to solve all problems, big and small – but, concretely, what would such a solution mean in the first place? Specially, what would the automation environment of the future look like? The following presentation introduces these issues, trying to reach a “systemic view ” of complexity.

This paper discusses what the future modeling environments could look like. To tackle with ever increasing complexity of process models, higher level of abstraction needs to be exploited. It is noticed that the most natural way to connect low-level models to high-level tools is simulation. Based on such semantic grounding, new description formalisms can perhaps be implemented. 1. NEW CHALLENGES Because of the fieldbuses, and because of the modern sensor technology, etc., the availability of the industrial processes has been enhanced considerably. There is an explosion of structureless data facing us. The problem is that there do not exist enough domain area experts that could analyze the data and rewrite the models for the processes appropriately. Automatic modeling systems would be invaluable – systems that could not only adapt the model parameters within a predetermined structural framework, but also determine the structures themselves without too much human intervention. The modeling problems are attacked by utilizing different kinds of description formalisms. One major approach is to define more and more general formalisms (like Java language) for system description: In such environments, anything can be expressed, but this means that large numbers of expressions are needed