BOOLEAN DERIVATIVES AND COMPUTATION OF CELLULAR AUTOMATA

Franco Bagnoli
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Franco Bagnoli: Dipartimento di Matematica Applicata, Università di Firenze, Firenze, I 50139, Italy

International Journal of Modern Physics C (IJMPC), 1992, vol. 03, issue 02, 307-320

Abstract: 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 analyzed, and expressions with fewer terms are generally found.

Keywords: Boolean Derivatives; Cellular Automata; Minimization of Boolean Functions; Multi-site Technique (search for similar items in EconPapers)
Date: 1992
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DOI: 10.1142/S0129183192000257

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