Thomas Worsch

Simulation of cellular automata

Abstract There exists quite a number of software packages for the simulation of cellular automata (CA). After a short review of the standard definition some modifications and extensions are discussed which have in particular proven to be useful or important for the use of CA as models of real phenomena. A survey of the features of several software packages for the simulation of CA is given. For several applications reasonably fast simulations require the use of parallel computers. For message passing systems connected by a reasonably fast network a domain decomposition approach and possible optimizations are described.

Programming Environments for Cellular Automata

Some modifications and generalizations of cellular automata are discussed which are sometimes useful in the modeling of real phenomena and which therefore have found their ways into some programming environment for cellular automata. In the second part several aspects are discussed with respect to which these programming environments can be compared.

The Firing Squad Synchronization Problem with Many Generals for One-Dimensional CA

The Firing Squad Synchronization Problem is one of the classical problems for cellular automata. In this paper we consider the case of more than one general. A synchronous and an asynchronous version of the problem are considered. In the latter case the generals may start their activities at different times. In the synchronous case there are optimumtime solutions. Very simple and elegant techniques for constructing one of them are the main contribution of this paper on the algorithmic side. For the asynchronous case an exact formula for the optimum synchronization time of each instance is derived. We prove that no CA can solve all instances in optimum time, but we describe a CA whose running time is very close to it; it only needs additional log n steps.

On Benchmarking Collective MPI Operations

This article concentrates on recent work on benchmarking collective operations with SKaMPI. The goal of the SKaMPI project is the creation of a database containing performance measurements of parallel computers in terms of MPI operations. These data support software developers in creating portable and fast programs. Existing algorithms for measuring the timing of collective operations are discussed and a new algorithm is presented, taking into account the differences of local clocks. Results of measurements on a Cray T3E/900 and an IBM RS 6000 SP are presented.

Linear Time Language Recognition on Cellular Automata with Restricted Communication

It is well-known that for classical one-dimensional one-way CA (OCA) it is possible to speed up language recognition times from (1 + r)n, r ∈ R + , to (1 + r/2)n. In this paper we show that this no longer holds for OCA in which a cell can comminucate only one bit (or more generally a fixed amount) of information to its neighbor in each step. For arbitrary real numbers r 2 > r 1 > 1 in time r 2 n 1-bit OCA can recognize strictly more languages than those operating in time r 1 n. Thus recognition times may increase by an arbitrarily large constant factor when restricting the communication to 1 bit. For two-way CA there is also an infinite hierarchy but it is not known whether it is as dense as for OCA. Furthermore it is shown that for communication restricted CA two-way flow of information can be much more powerful than an arbitrary number of additional communication bits.

Efficient Simulation of CA with Few Activities

Motivated by the wish to make large simulations of Bak’s sandpile model we investigate a simple method to simulate cellular automata with “few activities” efficiently on a computer.

Introduction to the special issue on cellular automata

Abstract In this introduction we review the basics of cellular automata and give a short survey of some areas of research concerning cellular automata. This is done to fit the papers of the present special issue into a general frame.

A perimeter—time CA for the queen bee problem

We present a CA for the so-called queen bee problem posed by Smith which is the problem of leader election in arbitrary patterns. The running time of the solution presented is within a factor of 2 of a lower bound.

Parallel Turing machines with one-head control units and cellular automata

Parallel Turing machines (Ptm) can be viewed as a generalization of cellular automata (Ca) where an additional measure called processor complexity can be defined which indicates the “amount of parallelism” used. In this paper Ptm are investigated with respect to their power as recognizers of formal languages. A combinatorial approach as well as diagonalization are used to obtain hierarchies of complexity classes for Ptm and Ca. In some cases it is possible to keep the space complexity of Ptm fixed. Thus for the first time it is possible to find hierarchies of complexity classes (though not Ca classes) which are completely contained in the class of languages recognizable by Ca with space complexity n and in polynomial time. A possible collapse of the time hierarchy for these Ca would therefore also imply some unexpected properties of Ptm.

On parallel Turing machines with multi-head control units

This paper deals with parallel Turing machines with multi-head control units on one or more tapes which can be considered as a generalization of cellular automata. We discuss the problem of finding an appropriate measure of space complexity. A definition is suggested which implies that the model is in the first machine class. It is shown that without loss of generality it suffices to consider only parallel Turing machines of certain normal forms.