Results 1  10
of
82
Characterizing Configuration Spaces of Simple Threshold Cellular Automata
 in SpringerVerlag LNCS series
, 2004
"... Abstract. We study herewith the simple threshold cellular automata (CA), as perhaps the simplest broad class of CA with nonadditive (i.e., nonlinear and nonaffine) local update rules. We characterize all possible computations of the most interesting rule for such CA, namely, the Majority (MAJ) ru ..."
Abstract

Cited by 16 (5 self)
 Add to MetaCart
Abstract. We study herewith the simple threshold cellular automata (CA), as perhaps the simplest broad class of CA with nonadditive (i.e., nonlinear and nonaffine) 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
A nonlinear dynamics perspective of Wolfram’s new kind of science. Part III: Predicting the unpredictable
 International Journal of Bifurcation and Chaos
, 2004
"... 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 justi ..."
Abstract

Cited by 13 (0 self)
 Add to MetaCart
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 threedimensional Euclidean space. In particular, Wolfram’s seductive idea of a “threshold of
Toward Reliable Algorithmic SelfAssembly of DNA Tiles: A FixedWidth Cellular Automaton Pattern NANO LETTERS
, 2007
"... Bottomup fabrication of nanoscale structures relies on chemical processes to direct selfassembly. The complexity, precision, and yield achievable by a onepot reaction are limited by our ability to encode assembly instructions into the molecules themselves. Nucleic acids provide a platform for inv ..."
Abstract

Cited by 13 (1 self)
 Add to MetaCart
Bottomup fabrication of nanoscale structures relies on chemical processes to direct selfassembly. The complexity, precision, and yield achievable by a onepot 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 onepot 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 selfassembly may be sufficient to create a wide range of complex objects in onepot reactions. The WatsonsCrick complementarity of DNA molecules allows one to design not only simple doublestranded helices but also complicated woven structures consisting of many DNA strands. 1 Welldesigned structures will selfassemble during annealing from a high initial temperature at which point all molecules are singlestranded to a lower final
Design of an autonomous DNA nanomechanical device capable of universal computation and universal translational motion
, 2004
"... Abstract. 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 ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
Abstract. 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 an autonomous DNA mechanical device capable of universal computation, by mimicking the operation of a universal Turing machine. Building on our prior theoretical design and prototype experimental construction of an autonomous unidirectional DNA walking device moving along a linear track, we present here the design of a nanomechanical DNA device that autonomously mimics the operation of a 2state 5color universal Turing machine. Our autonomous nanomechanical device, called an Autonomous DNA Turing Machine (ADTM), is thus capable of universal computation and hence complex translational motion, which we define as universal translational motion. 1
Small weakly universal Turing machines
"... Abstract. We give small universal Turing machines with statesymbol 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 ..."
Abstract

Cited by 7 (4 self)
 Add to MetaCart
Abstract. We give small universal Turing machines with statesymbol 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
Understanding a nontrivial cellular automaton by finding its simplest underlying communication protocol
 of Lecture Notes in Computer Science
, 2008
"... Abstract. In the present work we find a nontrivial communication protocol describing the dynamics of an elementary CA, and we prove that there are no simpler descriptions (protocols) for such CA. This is, to our knowledge, the first time such a result is obtained in the study of CAs. More precisely ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
Abstract. In the present work we find a nontrivial communication protocol describing the dynamics of an elementary CA, and we prove that there are no simpler descriptions (protocols) for such CA. This is, to our knowledge, the first time such a result is obtained in the study of CAs. More precisely, we divide the cells of Rule 218 into two groups and we describe (and therefore understand) its global dynamics by finding a protocol taking place between these two parts. We assume that x ∈ {0, 1} n is given to Alice while y ∈ {0, 1} n is given to Bob. Let us call z(x, y) ∈ {0, 1} the result of the dynamical interaction between the cells. We exhibit a protocol where Alice, instead of the n bits of x, sends 2⌈log(n) ⌉ + 1 bits to Bob allowing him to compute z(x, y). Roughly, she sends 2 particular positions of her string x. By proving that any oneround protocol computing z(x,y) must exchange at least 2⌈log(n) ⌉ − 5 bits, the optimality of our construction (up to a constant) is concluded. 1
Institutionalization through Reciprocal Habitalization and Typification
 Second NASA Workshop on Radical Agent Concepts (WRAC), NASA Goddard Spaceflight
, 2005
"... 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 notio ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
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.
Decidability and universality in symbolic dynamical systems
 Fund. Inform
"... Abstract. Many different definitions of computational universality for various types of dynamical systems have flourished since Turing’s work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical systems. Universality of a system is defined as un ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
Abstract. Many different definitions of computational universality for various types of dynamical systems have flourished since Turing’s work. We propose a general definition of universality that applies to arbitrary discrete time symbolic dynamical systems. Universality of a system is defined as undecidability of a modelchecking problem. For Turing machines, counter machines and tag systems, our definition coincides with the classical one. It yields, however, a new definition for cellular automata and subshifts. Our definition is robust with respect to initial condition, which is a desirable feature for physical realizability. We derive necessary conditions for undecidability and universality. For instance, a universal system must have a sensitive point and a proper subsystem. We conjecture that universal systems have infinite number of subsystems. We also discuss the thesis according to which computation should occur at the ‘edge of chaos ’ and we exhibit a universal chaotic system. 1.
Neocybernetics in biological systems
, 2006
"... 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. Pre ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
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 manmade ones that seem to be cybernetic. The word “biological ” in the title should be interpreted as “biological ” — 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 allembracing 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:
BioMed Central
, 2006
"... A novel approach to phylogenetic tree construction using stochastic optimization and clustering ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
A novel approach to phylogenetic tree construction using stochastic optimization and clustering