2,031 research outputs found
Bulking II: Classifications of Cellular Automata
This paper is the second part of a series of two papers dealing with bulking:
a way to define quasi-order on cellular automata by comparing space-time
diagrams up to rescaling. In the present paper, we introduce three notions of
simulation between cellular automata and study the quasi-order structures
induced by these simulation relations on the whole set of cellular automata.
Various aspects of these quasi-orders are considered (induced equivalence
relations, maximum elements, induced orders, etc) providing several formal
tools allowing to classify cellular automata
A guided tour of asynchronous cellular automata
Research on asynchronous cellular automata has received a great amount of
attention these last years and has turned to a thriving field. We survey the
recent research that has been carried out on this topic and present a wide
state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat
Canalization and control in automata networks: body segmentation in Drosophila melanogaster
We present schema redescription as a methodology to characterize canalization
in automata networks used to model biochemical regulation and signalling. In
our formulation, canalization becomes synonymous with redundancy present in the
logic of automata. This results in straightforward measures to quantify
canalization in an automaton (micro-level), which is in turn integrated into a
highly scalable framework to characterize the collective dynamics of
large-scale automata networks (macro-level). This way, our approach provides a
method to link micro- to macro-level dynamics -- a crux of complexity. Several
new results ensue from this methodology: uncovering of dynamical modularity
(modules in the dynamics rather than in the structure of networks),
identification of minimal conditions and critical nodes to control the
convergence to attractors, simulation of dynamical behaviour from incomplete
information about initial conditions, and measures of macro-level canalization
and robustness to perturbations. We exemplify our methodology with a well-known
model of the intra- and inter cellular genetic regulation of body segmentation
in Drosophila melanogaster. We use this model to show that our analysis does
not contradict any previous findings. But we also obtain new knowledge about
its behaviour: a better understanding of the size of its wild-type attractor
basin (larger than previously thought), the identification of novel minimal
conditions and critical nodes that control wild-type behaviour, and the
resilience of these to stochastic interventions. Our methodology is applicable
to any complex network that can be modelled using automata, but we focus on
biochemical regulation and signalling, towards a better understanding of the
(decentralized) control that orchestrates cellular activity -- with the
ultimate goal of explaining how do cells and tissues 'compute'
On some one-sided dynamics of cellular automata
A dynamical system consists of a space of all possible world states and a transformation of said space. Cellular automata are dynamical systems where the space is a set of one- or two-way infinite symbol sequences and the transformation is defined by a homogenous local rule. In the setting of cellular automata, the geometry of the underlying space allows one to define one-sided variants of some dynamical properties; this thesis considers some such one-sided dynamics of cellular automata.
One main topic are the dynamical concepts of expansivity and that of pseudo-orbit tracing property. Expansivity is a strong form of sensitivity to the initial conditions while pseudo-orbit tracing property is a type of approximability. For cellular automata we define one-sided variants of both of these concepts. We give some examples of cellular automata with these properties and prove, for example, that right-expansive cellular automata are chain-mixing. We also show that left-sided pseudo-orbit tracing property together with right-sided expansivity imply that a cellular automaton has the pseudo-orbit tracing property.
Another main topic is conjugacy. Two dynamical systems are conjugate if, in a dynamical sense, they are the same system. We show that for one-sided cellular automata conjugacy is undecidable. In fact the result is stronger and shows that the relations of being a factor or a susbsystem are undecidable, too
Compression-based investigation of the dynamical properties of cellular automata and other systems
A method for studying the qualitative dynamical properties of abstract
computing machines based on the approximation of their program-size complexity
using a general lossless compression algorithm is presented. It is shown that
the compression-based approach classifies cellular automata (CA) into clusters
according to their heuristic behavior, with these clusters showing a
correspondence with Wolfram's main classes of CA behavior. A compression based
method to estimate a characteristic exponent to detect phase transitions and
measure the resiliency or sensitivity of a system to its initial conditions is
also proposed. A conjecture regarding the capability of a system to reach
computational universality related to the values of this phase transition
coefficient is formulated. These ideas constitute a compression-based framework
for investigating the dynamical properties of cellular automata and other
systems.Comment: 28 pages. This version includes the conjecture relating the
transition coefficient to computational universality. Camera ready versio
The Integration of Connectionism and First-Order Knowledge Representation and Reasoning as a Challenge for Artificial Intelligence
Intelligent systems based on first-order logic on the one hand, and on
artificial neural networks (also called connectionist systems) on the other,
differ substantially. It would be very desirable to combine the robust neural
networking machinery with symbolic knowledge representation and reasoning
paradigms like logic programming in such a way that the strengths of either
paradigm will be retained. Current state-of-the-art research, however, fails by
far to achieve this ultimate goal. As one of the main obstacles to be overcome
we perceive the question how symbolic knowledge can be encoded by means of
connectionist systems: Satisfactory answers to this will naturally lead the way
to knowledge extraction algorithms and to integrated neural-symbolic systems.Comment: In Proceedings of INFORMATION'2004, Tokyo, Japan, to appear. 12 page
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