2,150 research outputs found
Simulating Three-Dimensional Hydrodynamics on a Cellular-Automata Machine
We demonstrate how three-dimensional fluid flow simulations can be carried
out on the Cellular Automata Machine 8 (CAM-8), a special-purpose computer for
cellular-automata computations. The principal algorithmic innovation is the use
of a lattice-gas model with a 16-bit collision operator that is specially
adapted to the machine architecture. It is shown how the collision rules can be
optimized to obtain a low viscosity of the fluid. Predictions of the viscosity
based on a Boltzmann approximation agree well with measurements of the
viscosity made on CAM-8. Several test simulations of flows in simple geometries
-- channels, pipes, and a cubic array of spheres -- are carried out.
Measurements of average flux in these geometries compare well with theoretical
predictions.Comment: 19 pages, REVTeX and epsf macros require
Two dimensional outflows for cellular automata with shuffle updates
In this paper, we explore the two-dimensional behavior of cellular automata
with shuffle updates. As a test case, we consider the evacuation of a square
room by pedestrians modeled by a cellular automaton model with a static floor
field. Shuffle updates are characterized by a variable associated to each
particle and called phase, that can be interpreted as the phase in the step
cycle in the frame of pedestrian flows. Here we also introduce a dynamics for
these phases, in order to modify the properties of the model. We investigate in
particular the crossover between low- and high-density regimes that occurs when
the density of pedestrians increases, the dependency of the outflow in the
strength of the floor field, and the shape of the queue in front of the exit.
Eventually we discuss the relevance of these results for pedestrians.Comment: 20 pages, 5 figures. v2: 16 pages, 5 figures; changed the title,
abstract and structure of the paper. v3: minor change
Qualitative Reachability in Stochastic BPA Games
We consider a class of infinite-state stochastic games generated by stateless
pushdown automata (or, equivalently, 1-exit recursive state machines), where
the winning objective is specified by a regular set of target configurations
and a qualitative probability constraint `>0' or `=1'. The goal of one player
is to maximize the probability of reaching the target set so that the
constraint is satisfied, while the other player aims at the opposite. We show
that the winner in such games can be determined in PTIME for the `>0'
constraint, and both in NP and coNP for the `=1' constraint. Further, we prove
that the winning regions for both players are regular, and we design algorithms
which compute the associated finite-state automata. Finally, we show that
winning strategies can be synthesized effectively.Comment: Submitted to Information and Computation. 48 pages, 3 figure
What Is a Macrostate? Subjective Observations and Objective Dynamics
We consider the question of whether thermodynamic macrostates are objective
consequences of dynamics, or subjective reflections of our ignorance of a
physical system. We argue that they are both; more specifically, that the set
of macrostates forms the unique maximal partition of phase space which 1) is
consistent with our observations (a subjective fact about our ability to
observe the system) and 2) obeys a Markov process (an objective fact about the
system's dynamics). We review the ideas of computational mechanics, an
information-theoretic method for finding optimal causal models of stochastic
processes, and argue that macrostates coincide with the ``causal states'' of
computational mechanics. Defining a set of macrostates thus consists of an
inductive process where we start with a given set of observables, and then
refine our partition of phase space until we reach a set of states which
predict their own future, i.e. which are Markovian. Macrostates arrived at in
this way are provably optimal statistical predictors of the future values of
our observables.Comment: 15 pages, no figure
Finite automata for caching in matrix product algorithms
A diagram is introduced for visualizing matrix product states which makes
transparent a connection between matrix product factorizations of states and
operators, and complex weighted finite state automata. It is then shown how one
can proceed in the opposite direction: writing an automaton that ``generates''
an operator gives one an immediate matrix product factorization of it. Matrix
product factorizations have the advantage of reducing the cost of computing
expectation values by facilitating caching of intermediate calculations. Thus
our connection to complex weighted finite state automata yields insight into
what allows for efficient caching in matrix product algorithms. Finally, these
techniques are generalized to the case of multiple dimensions.Comment: 18 pages, 19 figures, LaTeX; numerous improvements have been made to
the manuscript in response to referee feedbac
Boolean derivatives and computation of cellular automata
The derivatives of a Boolean function are defined up to any order. The Taylor
and MacLaurin expansions of a Boolean function are thus obtained. The last
corresponds to the ring sum expansion (RSE) of a Boolean function, and is a
more compact form than the usual canonical disjunctive form. For totalistic
functions the RSE allows the saving of a large number of Boolean operations.
The algorithm has natural applications to the simulations of cellular automata
using the multi site coding technique. Several already published algorithms are
analized, and expressions with fewer terms are generally found.Comment: 15 page
Extracting Boolean rules from CA patterns
A multiobjective genetic algorithm (GA) is introduced to identify both the neighborhood and the rule set in the form of a parsimonious Boolean expression for both one- and two-dimensional cellular automata (CA). Simulation results illustrate that the new algorithm performs well even when the patterns are corrupted by static and dynamic nois
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