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Period lengths of cellular automata \(cam\)-90 with memory. (English) Zbl 0865.68080

Summary: Cellular automata ca-90 have states 0 and 1, and their dynamics, driven by the local transition rule 90, can be simply represented with Laurent polynomials over a finite field \(F_2=\{0,1\}\). Cellular automata cam-90 with memory, whose configurations are pairs of those of ca-90, are introduced as a useful machinery to solve certain equations on configurations, in particular, to compute fixed or kernel configurations of ca-90. This paper defines a notion of linear dynamical systems with memory, states their basic properties, and then studies some period lengths of one-dimensional and two-dimensional cellular automata cam-90 with memory.

MSC:

68Q80 Cellular automata (computational aspects)
82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
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[1] DOI: 10.1007/BF01223745 · Zbl 0564.68038 · doi:10.1007/BF01223745
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