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The as you know, in discrete mathematics there is no limit concept, but there is a function denoted by the term derivative. This is due to the Boolean function expansion in a series similar to the Maclaurin series at the point 00… 0 or the Taylor series at an arbitrary point in space. The article uses the derivatives’ form according to Bohman. In practice, the differentiator is used for the Boolean function optimal expansion f(x1, x2, … , xn) into k variables. The criterion for the variables optimal exclusion is to exclude first the variables, upon switching which the Boolean function switches under the conditions maximum number. It is natural to ask which function differential is equal to itself, known for continuous functions as one of Euler’s problems. The article analyses a similar formulation concerning differential equations in Boolean variables. A solution is given in a specific Zhegalkin polynomial form. |
