Differential equations of addition (DEA) are of the following form:
where and are -bit unknown variables and , and are known variables. The symbols and denote addition modulo and bitwise exclusive-or respectively. The above equation is denoted by .
Let a set
for integer denote a system of DEA where is a polynomial in . It has been proved that the satisfiability of an arbitrary set of DEA is in the complexity class P when a brute force search requires an exponential time.
In 2013, some properties of a special form of DEA were reported by Chengqing Li et al., where and is assumed known. Essentially, the special DEA can be represented as . Based on the found properties, an algorithm for deriving was proposed and analyzed.[1]