Boolean differential equations

AbstractIn this paper, we define two differentials D(f) and Δ(f) for a boolean polynomial f, with n variables. D(f), for instance, is chosen in such a way that its roots are exactly those of f(x) = m(f), where m(f) is the minimum of f on Bn. Then D(f) ⩽ f. We first state different properties for the differentiation, which is shown to be a boolean algebraic operator, then solve three boolean differential equations, among which are: D(f) = θf(θ ϵ B), and the quadrature equation, D(f) = g