Mixed Integer Programming Models for Finite Automaton and Its Application to Additive Differential Patterns of Exclusive-Or

Inspired by Fu et al. work [12] on modeling the exclusive-or differential property of the modulo addition as an mixed-integer programming problem, we propose a method with which any finite automaton can be formulated as an mixed-integer programming model. Using this method, we show how to construct a mixed integer programming model whose feasible region is the set of all differential patterns (α, β, γ)’s, such that adp⊕(α, β → γ) = Prx,y[((x+α)⊕ (y+β))− (x⊕ y) = γ] > 0. We expect that this may be useful in automatic differential analysis with additive difference.