Inspired by Fu et al. work 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 's, such that ${\rm adp}^\oplus (\alpha,\beta\rightarrow\gamma)={\rm Pr} _ {x, y}[((x+\alpha)\oplus (y+\beta))-(x\oplus y)=\gamma]> 0$. We expect that this may be useful in automatic differential analysis with additive difference.