Continuous automaton

About: Continuous automaton is a research topic. Over the lifetime, 947 publications have been published within this topic receiving 17417 citations.

Cellular automaton rules conserving the number of active sites

Abstract: This paper shows how to determine all of the unidimensional two-state cellular automaton rules of a given number of inputs which conserve the number of active sites. These rules have to satisfy a necessary and sufficient condition. If the active sites are viewed as cells occupied by identical particles, these cellular automaton rules represent evolution operators of systems of identical interacting particles whose total number is conserved. Some of these rules, which allow motion in both directions, mimic ensembles of one-dimensional pseudorandom walkers. Numerical evidence indicates that the corresponding stochastic processes might be non-Gaussian.

Cellular automaton model for bidirectional traffic

Abstract: We investigate a cellular automaton (CA) model of traffic on a bidirectional two-lane road. Our model is an extension of the one-lane CA model of Nagel and Schreckenberg [J. Phys. I (France) 2, 2221 (1992)], modified to account for interactions mediated by passing, and for a distribution of vehicle speeds. We chose values for the various parameters to approximate the behavior of real traffic. The density-flow diagram for the bidirectional model is compared to that of a one-lane model, showing the interaction of the two lanes. Results were also compared to experimental data, showing close agreement. This model helps bridge the gap between simplified cellular automata models and the complexity of real-world traffic.

A stochastic cellular automaton modeling gliding and aggregation of myxobacteria

Abstract: The myxobacteria are ubiquitous soil bacteria which aggregate under starvation conditions and build fruiting bodies to survive. Until recently the mechanisms of their social gliding, aggregation, and fruiting body formation have not been well understood. In this paper a stochastic cellular automaton model is presented to describe and provide an understanding of how the bacteria manage to build higher organized structures. In the automaton myxobacteria move on a square grid with periodic boundary conditions. They respond to the four nearest neighbors of their frontal cell poles, mainly through two factors: slime and a diffusing chemoattractant; both are produced by the bacteria themselves. Simulations show the interdependence of the different mechanisms which finally cause aggregation. A simplified version of this model is formally approximated by a system of partial differential equations, a chemotaxis system. A related publication [SIAM J. Appl. Math., 61 (2000), pp. 183--212] deals with the first rigoro...

Phenomenology of glider collisions in cellular automaton Rule 54 and associated logical gates

Abstract: Rule 54, a two state, three neighbor cellular automaton in Wolfram’s systems of nomenclature, is less complex that Rule 110, but nevertheless possess a rich and complex dynamics. We provide a systematic and exhaustive analysis of glider behavior and interactions, including a catalog of collisions. Many of them shows promise are computational elements.

Robust safety of timed automata

Abstract: Timed automata are governed by an idealized semantics that assumes a perfectly precise behavior of the clocks. The traditional semantics is not robust because the slightest perturbation in the timing of actions may lead to completely different behaviors of the automaton. Following several recent works, we consider a relaxation of this semantics, in which guards on transitions are widened by Δ>0 and clocks can drift by ?>0. The relaxed semantics encompasses the imprecisions that are inevitably present in an implementation of a timed automaton, due to the finite precision of digital clocks. We solve the safety verification problem for this robust semantics: given a timed automaton and a set of bad states, our algorithm decides if there exist positive values for the parameters Δ and ? such that the timed automaton never enters the bad states under the relaxed semantics.