Continuous automaton

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

Modified Traffic Cellular Automaton for the Density Classification Task

Abstract: The density classification task asks to design a cellular automaton that converges to the uniform configuration that corresponds to the state that is in majority in the initial configuration. We investigate connections of this problem to state-conserving cellular automata. We propose a modified traffic CA that washes out finite islands in the same way as the Gacs, Kurdyumov and Levin automaton, but is also guaranteed to converge to a uniform configuration on rings of odd size. We find experimentally several good classifiers that are close to state-conserving cellular automata, and we observe that the best performing known density classifier by Wolz and de Oliveira is only a simple swap away from a state-conserving automaton.

Towards a framework for intuitive programming of cellular automata

Abstract: The ability to obtain complex global behaviour from simple local rules makes cellular automata an interesting platform for massively parallel computation. However, manually designing a cellular automaton to perform a given computation can be extremely difficult, and automated design techniques such as genetic programming have their limitations because of the absence of human intuition. In this paper, we propose elements of a framework whose goal is to make the manual synthesis of cellular automata rules exhibiting desired global characteristics more programmer-friendly, while maintaining the simplicity of local processing elements. Although many of the framework elements that we describe here are not new, we group them into a consistent framework and show that they can all be implemented on a traditional cellular automaton, which means that they are merely more human-friendly ways of describing simple cellular automata rules, and not foreign structures that require changing the traditional cellular automaton model.

RAP1, a Cellular Automaton Machine for Fluid Dynamics.

Abstract: A bstra ct. RAP l is a spec ial pur pose comp uter built to st udy lat tice gas models. It allows the simulation of any model using less t ha n 16 bits p er node , and interacti ons restricted to first and second nearest neighb ors on a 256 x 512 square lat t ice. T he t ime evolu t ion of the automaton is displayed in real time on a color monitor at a sp eed of 50 fr ames per second. 1. I nt roduction T he concept of cellu lar automata was introduced in the early fift ies by von Neumann and U lam 11] to st ud y the be havior and the organization of complex systems. A cellular automaton (CA) is a set of identical processors located on a regu lar lat tice and with limited connections with t he ir neighbors. For each time ste p, th e CA is described by the values of t he states of all the pro cessors. At time t + 1, all t he pro cessors comp ute in parallel t he ir new state as a given function of t heir st ate and t hose of t he con nected p ro-cessors at time t , Wolfram [2] has shown t hat very simp le one-d imensional CA wit h one-b it int ernal states may give extremely complicated be hav iors, as soon as each cell is connected to its first-and second-nearest neighb ors and its time evolut ion is given by a Boolean funct ion chosen within t he suitable set of Boolean functi ons of five Boolean var iables. T he CAM mac hines built at MIT by T. Toffoli [3] played a pr ominent par t in t he int erest for CA during the las t five years. These machines demonst rated t hat cheap , but very powerful, spe cia l-purpose comp uters can be buil t to st udy a wide class of CA. T hey have also shown the impact of dir ect visualization on t he study of very complex phe nomena. Duri ng the same t ime, several attempts were done in t he phys icist com-mu nity to find simp le ways to descr ibe and st udy the motion of a collection of int eracting particles [4,5]. In …

Polynomial-time verification of the observer property in abstractions

Abstract: This paper presents an algorithm to test if an abstraction obtained through natural projection has the observer property, without having to compute the abstraction. The original automaton and the set of events to be kept by the projection are inputs to the algorithm. An automaton, the verifier, is built such that the verification of the property becomes a verification of reachability of a special state. The complexity of the algorithm is polynomial in the size of the state space of the automaton. Two examples are presented to illustrate the algorithm.