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Zbl 1134.37312
Garcia, Luis David; Jarrah, Abdul Salam; Laubenbacher, Reinhard
Sequential dynamical systems over words. (English)
[J] Appl. Math. Comput. 174, No. 1, 500-510 (2006). ISSN 0096-3003

Summary: This paper is motivated by the theory of sequential dynamical systems (SDS), 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.

MSC 2000:: *37B10 Symbolic dynamics
68Q45 Formal languages
68U20 Simulation

Keywords: Sequential dynamical systems; Galois correspondence; Words; Dependency graph; Acyclic orientation; Dynamically equivalent systems

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