Chapter 10: Processes of Perception and Analysis

Section 11: Traditional Mathematics and Mathematical Formulas

Primitive [Boolean] functions

There are several possible choices of primitive functions that can be combined to represent any Boolean function. In DNF And, Or and Not are used. Nand = Not[And[##]] & alone is also sufficient, as shown on page 619 and further discussed on page 807. (It is indicated by in the main text.) The functions And, Xor and Not are equivalent to Times, Plus and 1 - # & for variables modulo 2, and in this case algebraic functions like PolynomialReduce can be used for minimization. (See also page 1102.)

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From Stephen Wolfram: A New Kind of Science [citation]