Boolean derivatives and computation of cellular automata

Details Boolean derivatives and computation of cellular automata Boolean derivatives and computation of cellular automata

1999-12-20

arxiv.org/abs/cond-mat/9912353v3

F. Bagnoli, Int. Journ.Mod. Phys. C, 3, 307-320 (1992)

Physics

Condensed Matter

15 pages

Scientific paper

10.1142/S0129183192000257

The derivatives of a Boolean function are defined up to any order. The Taylor and MacLaurin expansions of a Boolean function are thus obtained. The last corresponds to the ring sum expansion (RSE) of a Boolean function, and is a more compact form than the usual canonical disjunctive form. For totalistic functions the RSE allows the saving of a large number of Boolean operations. The algorithm has natural applications to the simulations of cellular automata using the multi site coding technique. Several already published algorithms are analized, and expressions with fewer terms are generally found.

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