A Max-Plus Model of Asynchronous Cellular Automata

This paper presents a new framework for asynchrony. This has its origins in our attempts to better harness the internal decision making process of cellular automata (CA). Thus, we show that a max-plus algebraic model of asynchrony arises naturally from the CA requirement that a cell receives the state of each neighbour before updating. The significant result is the existence of a bijective mapping between the asynchronous system and the synchronous system classically used to update cellular automata. Consequently, although the CA outputs look qualitatively different, when surveyed on "contours" of real time, the asynchronous CA replicates the synchronous CA. Moreover, this type of asynchrony is simple - it is characterised by the underlying network structure of the cells, and long-term behaviour is deterministic and periodic due to the linearity of max-plus algebra. The findings lead us to proffer max-plus algebra as: (i) a more accurate and efficient underlying timing mechanism for models of patterns seen in nature, and (ii) a foundation for promising extensions and applications.Comment: in Complex Systems (Complex Systems Publications Inc), Volume 23, Issue 4, 201

A guided tour of asynchronous cellular automata

Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat

An AER Spike-Processing Filter Simulator and Automatic VHDL Generator Based on Cellular Automata

Spike-based systems are neuro-inspired circuits implementations traditionally used for sensory systems or sensor signal processing. Address-Event- Representation (AER) is a neuromorphic communication protocol for transferring asynchronous events between VLSI spike-based chips. These neuro-inspired implementations allow developing complex, multilayer, multichip neuromorphic systems and have been used to design sensor chips, such as retinas and cochlea, processing chips, e.g. filters, and learning chips. Furthermore, Cellular Automata (CA) is a bio-inspired processing model for problem solving. This approach divides the processing synchronous cells which change their states at the same time in order to get the solution. This paper presents a software simulator able to gather several spike-based elements into the same workspace in order to test a CA architecture based on AER before a hardware implementation. Furthermore this simulator produces VHDL for testing the AER-CA into the FPGA of the USBAER AER-tool.Ministerio de Ciencia e Innovación TEC2009-10639-C04-0

Visual Spike-based Convolution Processing with a Cellular Automata Architecture

this paper presents a first approach for implementations which fuse the Address-Event-Representation (AER) processing with the Cellular Automata using FPGA and AER-tools. This new strategy applies spike-based convolution filters inspired by Cellular Automata for AER vision processing. Spike-based systems are neuro-inspired circuits implementations traditionally used for sensory systems or sensor signal processing. AER is a neuromorphic communication protocol for transferring asynchronous events between VLSI spike-based chips. These neuro-inspired implementations allow developing complex, multilayer, multichip neuromorphic systems and have been used to design sensor chips, such as retinas and cochlea, processing chips, e.g. filters, and learning chips. Furthermore, Cellular Automata is a bio-inspired processing model for problem solving. This approach divides the processing synchronous cells which change their states at the same time in order to get the solution.Ministerio de Educación y Ciencia TEC2006-11730-C03-02Ministerio de Ciencia e Innovación TEC2009-10639-C04-02Junta de Andalucía P06-TIC-0141

Coxeter Groups and Asynchronous Cellular Automata

The dynamics group of an asynchronous cellular automaton (ACA) relates properties of its long term dynamics to the structure of Coxeter groups. The key mathematical feature connecting these diverse fields is involutions. Group-theoretic results in the latter domain may lead to insight about the dynamics in the former, and vice-versa. In this article, we highlight some central themes and common structures, and discuss novel approaches to some open and open-ended problems. We introduce the state automaton of an ACA, and show how the root automaton of a Coxeter group is essentially part of the state automaton of a related ACA.Comment: 10 pages, 4 figure