3,949 research outputs found
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
Deterministic Computations Whose History Is Independent of the Order of Asynchronous Updating
Consider a network of processors (sites) in which each site x has a finite set N(x) of neighbors. There is a transition function f that for each site x computes the next state ξ(x) from the states in N(x). But these transitions (updates) are applied in arbitrary order, one or many at a time. If the state of site x at time t is η(x; t) then let us define the sequence ζ(x; 0); ζ(x; 1), ... by taking the sequence η(x; 0),η(x; 1), ... , and deleting each repetition, i.e. each element equal to the preceding one. The function f is said to have invariant histories if the sequence ζ(x; i), (while it lasts, in case it is finite) depends only on the initial configuration, not on the order of updates.
This paper shows that though the invariant history property is typically undecidable, there is a useful simple sufficient condition, called commutativity: For any configuration, for any pair x; y of neighbors, if the updating would change both Îľ(x) and Îľ(y) then the result of updating first x and then y is the same as the result of doing this in the reverse order. This fact is derivable from known results on the confluence of term-rewriting systems but the self-contained proof given here may be justifiable.National Science Foundation (CCR-920484
Deterministic computations whose history is independent of the order of asynchronous updating
Consider a network of processors (sites) in which each site x has a finite
set N(x) of neighbors. There is a transition function f that for each site x
computes the next state \xi(x) from the states in N(x). But these transitions
(updates) are applied in arbitrary order, one or many at a time. If the state
of site x at time t is \eta(x,t) then let us define the sequence \zeta(x,0),
\zeta(x,1), ... by taking the sequence \eta(x,0), \eta(x,1), ..., and deleting
repetitions. The function f is said to have invariant histories if the sequence
\zeta(x,i), (while it lasts, in case it is finite) depends only on the initial
configuration, not on the order of updates.
This paper shows that though the invariant history property is typically
undecidable, there is a useful simple sufficient condition, called
commutativity: For any configuration, for any pair x,y of neighbors, if the
updating would change both \xi(x) and \xi(y) then the result of updating first
x and then y is the same as the result of doing this in the reverse order
Evolutionary Games and Computer Simulations
The prisoner's dilemma has long been considered the paradigm for studying the
emergence of cooperation among selfish individuals. Because of its importance,
it has been studied through computer experiments as well as in the laboratory
and by analytical means. However, there are important differences between the
way a system composed of many interacting elements is simulated by a digital
machine and the manner in which it behaves when studied in real experiments. In
some instances, these disparities can be marked enough so as to cast doubt on
the implications of cellular automata type simulations for the study of
cooperation in social systems. In particular, if such a simulation imposes
space-time granularity, then its ability to describe the real world may be
compromised. Indeed, we show that the results of digital simulations regarding
territoriality and cooperation differ greatly when time is discrete as opposed
to continuous.Comment: 8 pages. Also available through anonymous ftp from parcftp.xerox.com
in the directory /pub/dynamics as pdilemma.p
A Max-Plus Model of Asynchronous Cellular Automata
This paper presents a new framework for asynchrony. This has its origins in
our attempts to better harness the internal decision making process of cellular
automata (CA). Thus, we show that a max-plus algebraic model of asynchrony
arises naturally from the CA requirement that a cell receives the state of each
neighbour before updating. The significant result is the existence of a
bijective mapping between the asynchronous system and the synchronous system
classically used to update cellular automata. Consequently, although the CA
outputs look qualitatively different, when surveyed on "contours" of real time,
the asynchronous CA replicates the synchronous CA. Moreover, this type of
asynchrony is simple - it is characterised by the underlying network structure
of the cells, and long-term behaviour is deterministic and periodic due to the
linearity of max-plus algebra. The findings lead us to proffer max-plus algebra
as: (i) a more accurate and efficient underlying timing mechanism for models of
patterns seen in nature, and (ii) a foundation for promising extensions and
applications.Comment: in Complex Systems (Complex Systems Publications Inc), Volume 23,
Issue 4, 201
Parallelization of a Dynamic Monte Carlo Algorithm: a Partially Rejection-Free Conservative Approach
We experiment with a massively parallel implementation of an algorithm for
simulating the dynamics of metastable decay in kinetic Ising models. The
parallel scheme is directly applicable to a wide range of stochastic cellular
automata where the discrete events (updates) are Poisson arrivals. For high
performance, we utilize a continuous-time, asynchronous parallel version of the
n-fold way rejection-free algorithm. Each processing element carries an lxl
block of spins, and we employ the fast SHMEM-library routines on the Cray T3E
distributed-memory parallel architecture. Different processing elements have
different local simulated times. To ensure causality, the algorithm handles the
asynchrony in a conservative fashion. Despite relatively low utilization and an
intricate relationship between the average time increment and the size of the
spin blocks, we find that for sufficiently large l the algorithm outperforms
its corresponding parallel Metropolis (non-rejection-free) counterpart. As an
example application, we present results for metastable decay in a model
ferromagnetic or ferroelectric film, observed with a probe of area smaller than
the total system.Comment: 17 pages, 7 figures, RevTex; submitted to the Journal of
Computational Physic
- …