Showing papers on "Continuous automaton published in 2018"
TL;DR: In this article, the authors characterized measures and sets of measures that can be reached as limit points after iterating a cellular automaton on a simple initial measure, and showed that these computability conditions are sufficient by constructing a CA with auxiliary states in order to perform computations.
Abstract: The asymptotic behaviour of a cellular automaton iterated on a random configuration is well described by
its limit probability measure(s). In this paper, we characterise measures and sets of measures that can be reached as
limit points after iterating a cellular automaton on a simple initial measure.
In addition to classical topological constraints, we exhibit necessary computational obstructions. With an additional
hypothesis of connectivity, we show these computability conditions are sufficient by constructing a cellular automaton
realising these sets, using auxiliary states in order to perform computations. Adapting this construction, we obtain a
similar characterisation for the Ces\`aro mean convergence, a Rice theorem on the sets of limit points, and we are able
to perform computation on the set of measures, i.e. the cellular automaton converges towards a set of limit points that
depends on the initial measure. Last, under non-surjective hypotheses, it is possible to remove auxiliary states from
the construction.
13 citations
TL;DR: In this article, a non-Markovian lattice-gas cellular automata model for moving agents with memory is proposed, where the reorientation probabilities are derived from velocity autocorrelation functions that are given a priori; in that respect their approach is ''data-driven''.
Abstract: Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits non-trivial temporal decay of velocity autocorrelation functions. This means that the corresponding dynamics is characterized by memory effects that slowly decay in time. Motivated by this we construct non-Markovian lattice-gas cellular automata models for moving agents with memory. For this purpose the reorientation probabilities are derived from velocity autocorrelation functions that are given a priori; in that respect our approach is `data-driven'. Particular examples we consider are velocity correlations that decay exponentially or as power laws, where the latter functions generate anomalous diffusion. The computational efficiency of cellular automata combined with our analytical results paves the way to explore the relevance of memory and anomalous diffusion for the dynamics of interacting cell populations, like confluent cell monolayers and cell clustering.
9 citations
TL;DR: This paper proves that, in fact, no connected reversible Mealy automaton of prime size can generate an infinite Burnside group and explains how the method can be applied for some Mealy Automata of non prime size.
4 citations
TL;DR: This paper presents a 3-state asynchronous cellular automaton (CA) that requires merely two transition rules to achieve computational universality.
Abstract: This paper presents a 3-state asynchronous CA that requires merely two transition rules to achieve computational universality. This universality is achieved by embedding Priese’s delay-insensitive circuit elements, called the E-element and the K-element, on the cell space of a so-called Brownian CA, which is an asynchronous CA containing local configurations that conduct a random walk in the circuit topology.