2,012 research outputs found
Shift-Symmetric Configurations in Two-Dimensional Cellular Automata: Irreversibility, Insolvability, and Enumeration
The search for symmetry as an unusual yet profoundly appealing phenomenon,
and the origin of regular, repeating configuration patterns have long been a
central focus of complexity science and physics. To better grasp and understand
symmetry of configurations in decentralized toroidal architectures, we employ
group-theoretic methods, which allow us to identify and enumerate these inputs,
and argue about irreversible system behaviors with undesired effects on many
computational problems. The concept of so-called configuration shift-symmetry
is applied to two-dimensional cellular automata as an ideal model of
computation. Regardless of the transition function, the results show the
universal insolvability of crucial distributed tasks, such as leader election,
pattern recognition, hashing, and encryption. By using compact enumeration
formulas and bounding the number of shift-symmetric configurations for a given
lattice size, we efficiently calculate the probability of a configuration being
shift-symmetric for a uniform or density-uniform distribution. Further, we
devise an algorithm detecting the presence of shift-symmetry in a
configuration.
Given the resource constraints, the enumeration and probability formulas can
directly help to lower the minimal expected error and provide recommendations
for system's size and initialization. Besides cellular automata, the
shift-symmetry analysis can be used to study the non-linear behavior in various
synchronous rule-based systems that include inference engines, Boolean
networks, neural networks, and systolic arrays.Comment: 22 pages, 9 figures, 2 appendice
A Survey of Cellular Automata: Types, Dynamics, Non-uniformity and Applications
Cellular automata (CAs) are dynamical systems which exhibit complex global
behavior from simple local interaction and computation. Since the inception of
cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention
of several researchers over various backgrounds and fields for modelling
different physical, natural as well as real-life phenomena. Classically, CAs
are uniform. However, non-uniformity has also been introduced in update
pattern, lattice structure, neighborhood dependency and local rule. In this
survey, we tour to the various types of CAs introduced till date, the different
characterization tools, the global behaviors of CAs, like universality,
reversibility, dynamics etc. Special attention is given to non-uniformity in
CAs and especially to non-uniform elementary CAs, which have been very useful
in solving several real-life problems.Comment: 43 pages; Under review in Natural Computin
Shift-Symmetric Configurations in Two-Dimensional Cellular Automata: Irreversibility, Insolvability, and Enumeration
The search for symmetry as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have been for a long time a central focus of complexity science, and physics.
Here, we introduce group-theoretic concepts to identify and enumerate the symmetric inputs, which result in irreversible system behaviors with undesired effects on many computational tasks. The concept of so-called configuration shift-symmetry is applied on two-dimensional cellular automata as an ideal model of computation. The results show the universal insolvability of “non-symmetric” tasks regardless of the transition function. By using a compact enumeration formula and bounding the number of shift-symmetric configurations for a given lattice size, we efficiently calculate how likely a configuration randomly generated from a uniform or density-uniform distribution turns shift-symmetric. Further, we devise an algorithm detecting the presence of shift-symmetry in a configuration.
The enumeration and probability formulas can directly help to lower the minimal expected error for many crucial (non-symmetric) distributed problems, such as leader election, edge detection, pattern recognition, convex hull/minimum bounding rectangle, and encryption. Besides cellular automata, the shift-symmetry analysis can be used to study the non-linear behavior in various synchronous rule-based systems that include inference engines, Boolean networks, neural networks, and systolic arrays
Simple and Efficient Local Codes for Distributed Stable Network Construction
In this work, we study protocols so that populations of distributed processes
can construct networks. In order to highlight the basic principles of
distributed network construction we keep the model minimal in all respects. In
particular, we assume finite-state processes that all begin from the same
initial state and all execute the same protocol (i.e. the system is
homogeneous). Moreover, we assume pairwise interactions between the processes
that are scheduled by an adversary. The only constraint on the adversary
scheduler is that it must be fair. In order to allow processes to construct
networks, we let them activate and deactivate their pairwise connections. When
two processes interact, the protocol takes as input the states of the processes
and the state of the their connection and updates all of them. Initially all
connections are inactive and the goal is for the processes, after interacting
and activating/deactivating connections for a while, to end up with a desired
stable network. We give protocols (optimal in some cases) and lower bounds for
several basic network construction problems such as spanning line, spanning
ring, spanning star, and regular network. We provide proofs of correctness for
all of our protocols and analyze the expected time to convergence of most of
them under a uniform random scheduler that selects the next pair of interacting
processes uniformly at random from all such pairs. Finally, we prove several
universality results by presenting generic protocols that are capable of
simulating a Turing Machine (TM) and exploiting it in order to construct a
large class of networks.Comment: 43 pages, 7 figure
Dynamic neighbourhood cellular automata.
We propose a definition of cellular automaton in which each cell can change its neighbourhood during a computation. This is done locally by looking not farther than neighbours of neighbours and the number of links remains bounded by a constant throughout. We suggest that dynamic neighbourhood cellular automata can serve as a theoretical model in studying algorithmic and computational complexity issues of ubiquitous computations. We illustrate our approach by giving an optimal, logarithmic time solution of the Firing Squad Synchronization problem in this setting
Modelling Opinion Formation with Physics Tools: Call for Closer Link with Reality
The growing field of studies of opinion formation using physical formalisms and computer simulation based tools suffers from relative lack of connection to the 'real world' societal behaviour. Such sociophysics research should aim at explaining observations or at proposing new ones. Unfortunately, this is not always the case, as many works concentrate more on the models themselves than on the social phenomena. Moreover, the simplifications proposed in simulations often sacrifice realism on the altar of computability. There are several ways to improve the value of the research, the most important by promoting truly multidisciplinary cooperation between physicists aiming to describe social phenomena and sociologists studying the phenomena in the field. In the specific case of modelling of opinion formation there are a few technical ideas which might bring the computer models much closer to reality, and therefore to improve the predictive value of the sociophysics approach.Methodology, Agent Based Social Simulation, Qualitative Analysis; Evidence; Conditions of Application
Elements of the Theory of Dynamic Networks
The challenge of computing in a highly dynamic environment.</jats:p
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