17,558 research outputs found
Computations on Nondeterministic Cellular Automata
The work is concerned with the trade-offs between the dimension and the time
and space complexity of computations on nondeterministic cellular automata. It
is proved, that
1). Every NCA \Cal A of dimension , computing a predicate with time
complexity T(n) and space complexity S(n) can be simulated by -dimensional
NCA with time and space complexity and
by -dimensional NCA with time and space complexity .
2) For any predicate and integer if \Cal A is a fastest
-dimensional NCA computing with time complexity T(n) and space
complexity S(n), then .
3). If is time complexity of a fastest -dimensional NCA
computing predicate then T_{r+1,P} &=O((T_{r,P})^{1-r/(r+1)^2}),
T_{r-1,P} &=O((T_{r,P})^{1+2/r}). Similar problems for deterministic CA are
discussed.Comment: 18 pages in AmsTex, 3 figures in PostScrip
Design Implications of Model-Generated Urban Data
Published by the Architectural Research Centers Consortium under the terms of the Attribution-NonCommercial-ShareAlike 4.0 International license.The staggering complexity of urban environment and long timescales in the causal mechanisms prevent designers to fully understand the implications of their design interventions. In order to investigate these causal mechanisms and provide measurable trends, a model that partially replicates urban complexity has been developed. Using a cellular automata approach to model land use types and markets for products, services, labour and property, the model has enabled numerical experiments to be carried out. The results revealed causal mechanisms and performance metrics obtained in a much shorter timescale than the real-life processes, pointing to a number of design implications for urban environments.Peer reviewedFinal Published versio
Statistical Mechanics of Surjective Cellular Automata
Reversible cellular automata are seen as microscopic physical models, and
their states of macroscopic equilibrium are described using invariant
probability measures. We establish a connection between the invariance of Gibbs
measures and the conservation of additive quantities in surjective cellular
automata. Namely, we show that the simplex of shift-invariant Gibbs measures
associated to a Hamiltonian is invariant under a surjective cellular automaton
if and only if the cellular automaton conserves the Hamiltonian. A special case
is the (well-known) invariance of the uniform Bernoulli measure under
surjective cellular automata, which corresponds to the conservation of the
trivial Hamiltonian. As an application, we obtain results indicating the lack
of (non-trivial) Gibbs or Markov invariant measures for "sufficiently chaotic"
cellular automata. We discuss the relevance of the randomization property of
algebraic cellular automata to the problem of approach to macroscopic
equilibrium, and pose several open questions.
As an aside, a shift-invariant pre-image of a Gibbs measure under a
pre-injective factor map between shifts of finite type turns out to be always a
Gibbs measure. We provide a sufficient condition under which the image of a
Gibbs measure under a pre-injective factor map is not a Gibbs measure. We point
out a potential application of pre-injective factor maps as a tool in the study
of phase transitions in statistical mechanical models.Comment: 50 pages, 7 figure
Counter Machines and Distributed Automata: A Story about Exchanging Space and Time
We prove the equivalence of two classes of counter machines and one class of
distributed automata. Our counter machines operate on finite words, which they
read from left to right while incrementing or decrementing a fixed number of
counters. The two classes differ in the extra features they offer: one allows
to copy counter values, whereas the other allows to compute copyless sums of
counters. Our distributed automata, on the other hand, operate on directed path
graphs that represent words. All nodes of a path synchronously execute the same
finite-state machine, whose state diagram must be acyclic except for
self-loops, and each node receives as input the state of its direct
predecessor. These devices form a subclass of linear-time one-way cellular
automata.Comment: 15 pages (+ 13 pages of appendices), 5 figures; To appear in the
proceedings of AUTOMATA 2018
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