9,338 research outputs found
A compact topology for sand automata
In this paper, we exhibit a strong relation between the sand automata
configuration space and the cellular automata configuration space. This
relation induces a compact topology for sand automata, and a new context in
which sand automata are homeomorphic to cellular automata acting on a specific
subshift. We show that the existing topological results for sand automata,
including the Hedlund-like representation theorem, still hold. In this context,
we give a characterization of the cellular automata which are sand automata,
and study some dynamical behaviors such as equicontinuity. Furthermore, we deal
with the nilpotency. We show that the classical definition is not meaningful
for sand automata. Then, we introduce a suitable new notion of nilpotency for
sand automata. Finally, we prove that this simple dynamical behavior is
undecidable
A compact topology for sand automata
In this paper, we exhibit a strong relation between the sand automata configuration space and the cellular automata configuration space. This relation induces a compact topology for sand automata, and a new context in which sand automata are homeomorphic to cellular automata acting on a specific subshift. We show that the existing topological results for sand automata, including the Hedlund-like representation theorem, still hold. In this context, we give a characterization of the cellular automata which are sand automata, and study some dynamical behaviors such as equicontinuity. Furthermore, we deal with the nilpotency. We show that the classical definition is not meaningful for sand automata. Then, we introduce a suitable new notion of nilpotency for sand automata. Finally, we prove that this simple dynamical behavior is undecidable
Self-Organized States in Cellular Automata: Exact Solution
The spatial structure, fluctuations as well as all state probabilities of
self-organized (steady) states of cellular automata can be found (almost)
exactly and {\em explicitly} from their Markovian dynamics. The method is shown
on an example of a natural sand pile model with a gradient threshold.Comment: 4 pages (REVTeX), incl. 2 figures (PostScript
Cellular automata and self-organized criticality
Cellular automata provide a fascinating class of dynamical systems capable of
diverse complex behavior. These include simplified models for many phenomena
seen in nature. Among other things, they provide insight into self-organized
criticality, wherein dissipative systems naturally drive themselves to a
critical state with important phenomena occurring over a wide range of length
and time scales.Comment: 23 pages, 12 figures (most in color); uses sprocl.tex; chapter
submitted for "Some new directions in science on computers," G. Bhanot, S.
Chen, and P. Seiden, ed
Minimizing finite automata is computationally hard
It is known that deterministic finite automata (DFAs) can be algorithmically minimized, i.e., a DFA M can be converted to an equivalent DFA M' which has a minimal number of states. The minimization can be done efficiently [6]. On the other hand, it is known that unambiguous finite automata (UFAs) and nondeterministic finite automata (NFAs) can be algorithmically minimized too, but their minimization problems turn out to be NP-complete and PSPACE-complete [8]. In this paper, the time complexity of the minimization problem for two restricted types of finite automata is investigated. These automata are nearly deterministic, since they only allow a small amount of non determinism to be used. On the one hand, NFAs with a fixed finite branching are studied, i.e., the number of nondeterministic moves within every accepting computation is bounded by a fixed finite number. On the other hand, finite automata are investigated which are essentially deterministic except that there is a fixed number of different initial states which can be chosen nondeterministically. The main result is that the minimization problems for these models are computationally hard, namely NP-complete. Hence, even the slightest extension of the deterministic model towards a nondeterministic one, e.g., allowing at most one nondeterministic move in every accepting computation or allowing two initial states instead of one, results in computationally intractable minimization problems
An Invitation to Number-Conserving Cellular Automata
Number-conserving cellular automata are discrete dynamical systems that
simulate interacting particles like e.g. grains of sand. In an earlier paper, I
had already derived a uniform construction for all transition rules of
one-dimensional number-conserving automata. Here I describe in greater detail
how one can simulate the automata on a computer and how to find interesting
rules. I show several rules that I have found this way and also some theorems
about the space of number-conserving automata.Comment: 15 pages, 4 figure
Xtoys: cellular automata on xwindows
Xtoys is a collection of xwindow programs for demonstrating simulations of
various statistical models. Included are xising, for the two dimensional Ising
model, xpotts, for the -state Potts model, xautomalab, for a fairly general
class of totalistic cellular automata, xsand, for the Bak-Tang-Wiesenfield
model of self organized criticality, and xfires, a simple forest fire
simulation. The programs should compile on any machine supporting xwindows.Comment: 4 pages, one figure, uuencoded compressed postscript Contribution to
Lattice '95 Also available at
http://penguin.phy.bnl.gov/www/papers/BNL-62123.ps.Z Programs available at
http://penguin.phy.bnl.gov/www/xtoys/xtoys.htm
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