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On periods and equilibria of computational sequential systems. (English) Zbl 1429.68167

Summary: In this paper, we show that sequential systems with (Boolean) maxterms and minterms as global evolution operators can present orbits of any period. Besides, we prove that periodic orbits with different periods greater than or equal to 2 can coexist. Nevertheless, when a sequential dynamical system has fixed points, we demonstrate that periodic orbits of other periods cannot appear. Finally, we provide conditions to obtain a fixed point theorem in this context. This work provides a relevant advance in the knowledge of the dynamics of such systems which constitute one of the most effective mathematical tools to model computational processes and other phenomena from other Sciences. Moreover, the ideas developed here could help to obtain similar results for other related systems.

MSC:

68R10 Graph theory (including graph drawing) in computer science
37B15 Dynamical aspects of cellular automata
37E15 Combinatorial dynamics (types of periodic orbits)
68Q06 Networks and circuits as models of computation; circuit complexity
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