Sequential dynamical systems over words

doi:10.1016/j.amc.2005.04.101

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Sequential dynamical systems over words

2006-03-01

PRE

Garcia, LD

Abdul Salam Jarrah

Reinhard Laubenbacher

DOI：10.1016/j.amc.2005.04.101

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Abstract

En 中文

This paper is motivated by the theory of sequential dynamical systems (SIDS), developed as a basis for a mathematical theory of computer simulation. A sequential dynamical system is a collection of symmetric Boolean local update functions, with the update order determined by a permutation of the Boolean variables. In this paper, the notion of SDS is generalized to allow arbitrary functions over a general finite field, with the update schedule given by an arbitrary word on the variables. The paper contains generalizations of some of the known results about SDS with permutation update schedules. In particular, an upper bound on the number of different SDS over words of a given length is proved and open problems are discussed. (c) 2005 Elsevier Inc. All rights reserved.

Keywords:

sequential dynamical systems

Galois correspondence

words

dependency graph

acyclic orientation

dynamically equivalent systems