Revisiting the Rice Theorem of Cellular Automata

A cellular automaton is a parallel synchronous computing model, which consists in a juxtaposition of finite automata whose state evolves according to that of their neighbors. It induces a dynamical system on the set of configurations, i.e. the infinite sequences of cell states. The limit set of the cellular automaton is the set of configurations which can be reached arbitrarily late in the evolution. In this paper, we prove that all properties of limit sets of cellular automata with binary-state cells are undecidable, except surjectivity. This is a refinement of the classical "Rice Theorem" that Kari proved on cellular automata with arbitrary state sets.Comment: 12 pages conference STACS'1

Parallel Cellular Automata: A Model Program for Computational Science

We develop a model program for parallel execution of cellular automata on a multicomputer. The model program is then adapted for simulation of forest fires and numerical solution of Laplace\u27s equation for stationary heat flow. The performance of the parallel program is analyzed and measured on a Computing Surface configured as a matrix of transputers with distributed memory

Ultimate Traces of Cellular Automata

A cellular automaton (CA) is a parallel synchronous computing model, which consists in a juxtaposition of finite automata (cells) whose state evolves according to that of their neighbors. Its trace is the set of infinite words representing the sequence of states taken by some particular cell. In this paper we study the ultimate trace of CA and partial CA (a CA restricted to a particular subshift). The ultimate trace is the trace observed after a long time run of the CA. We give sufficient conditions for a set of infinite words to be the trace of some CA and prove the undecidability of all properties over traces that are stable by ultimate coincidence.Comment: 12 pages + 5 of appendix conference STACS'1

Facilitating arrhythmia simulation: the method of quantitative cellular automata modeling and parallel running

BACKGROUND: Many arrhythmias are triggered by abnormal electrical activity at the ionic channel and cell level, and then evolve spatio-temporally within the heart. To understand arrhythmias better and to diagnose them more precisely by their ECG waveforms, a whole-heart model is required to explore the association between the massively parallel activities at the channel/cell level and the integrative electrophysiological phenomena at organ level. METHODS: We have developed a method to build large-scale electrophysiological models by using extended cellular automata, and to run such models on a cluster of shared memory machines. We describe here the method, including the extension of a language-based cellular automaton to implement quantitative computing, the building of a whole-heart model with Visible Human Project data, the parallelization of the model on a cluster of shared memory computers with OpenMP and MPI hybrid programming, and a simulation algorithm that links cellular activity with the ECG. RESULTS: We demonstrate that electrical activities at channel, cell, and organ levels can be traced and captured conveniently in our extended cellular automaton system. Examples of some ECG waveforms simulated with a 2-D slice are given to support the ECG simulation algorithm. A performance evaluation of the 3-D model on a four-node cluster is also given. CONCLUSIONS: Quantitative multicellular modeling with extended cellular automata is a highly efficient and widely applicable method to weave experimental data at different levels into computational models. This process can be used to investigate complex and collective biological activities that can be described neither by their governing differentiation equations nor by discrete parallel computation. Transparent cluster computing is a convenient and effective method to make time-consuming simulation feasible. Arrhythmias, as a typical case, can be effectively simulated with the methods described

Developing Tools for Networks of Processors

A great deal of research eort is currently being made in the realm of so called natural computing. Natural computing mainly focuses on the denition, formal description, analysis, simulation and programming of new models of computation (usually with the same expressive power as Turing Machines) inspired by Nature, which makes them particularly suitable for the simulation of complex systems.Some of the best known natural computers are Lindenmayer systems (Lsystems, a kind of grammar with parallel derivation), cellular automata, DNA computing, genetic and evolutionary algorithms, multi agent systems, arti- cial neural networks, P-systems (computation inspired by membranes) and NEPs (or networks of evolutionary processors). This chapter is devoted to this last model

OpenCAL++: An object-oriented architecture for transparent parallel execution of cellular automata models

Cellular Automata (CA) models, initially studied by John von Neumann, have been developed by numerous researchers and applied in both academic and scientific fields. Thanks to their local and independent rules, simulations of complex systems can be easily implemented based on CA modelling on parallel machines. However, due to the heterogeneity of the components - from the hardware to the software perspective-the various possible scenarios running parallelism in today’s architectures can pose a challenge in such implementations, making it difficult to exploit. This paper presents OpenCAL++, a transparent and efficient object-oriented platform for the parallel execution of cellular automata models. The architecture of OpenCAL++ ensures the modeller a fully transparent parallel execution and a strong ”separation of concerns” between the execution parallelism issues and the model implementation. The code implementing the Cellular Automata model remains the same whether the execution performs in a shared-, distributed-memory or a GPGPU context, irrespective of the optimizations adopted. To this aim, the object-oriented paradigm has been intensely exploited. As well as the OpenCAL++ architecture, we present the description of a simple Cellular Automata model implementation for illustrative purposes.This research was funded by the Italian “ICSC National Center for HPC, Big Data and Quantum Computing” Project, CN00000013 (approved under the Call M42C –Investment 1.4 – Avvisto “Centri Nazionali” – D.D. n. 3138 of 16.12.2021, admitted to financing with MUR Decree n. 1031 of 06.17.2022)Peer ReviewedPostprint (author's final draft

Parallel Genetic Algorithms for calibrating Cellular Automata models: Application to lava flows

Cellular Automata are highly nonlinear dynamical systems which are suitable for simulating natural phenomena whose behaviour may be specified in terms of local interactions. The Cellular Automata model SCIARA, developed for the simulation of lava flows, demonstrated to be able to reproduce the behaviour of Etnean events. However, in order to apply the model for the prediction of future scenarios, a thorough calibrating phase is required. This work presents the application of Genetic Algorithms, general-purpose search algorithms inspired to natural selection and genetics, for the parameters optimisation of the modelSCIARA. Difficulties due to the elevated computational time suggested the adoption a Master-Slave Parallel Genetic Algorithm for the calibration of the model with respect to the 2001 Mt. Etna eruption. Results demonstrated the usefulness of the approach, both in terms of computing time and quality of performed simulations