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A special case of this question and another question What is the complexity of solving system of binary quadratic equations modulo $3$? $f_i(x_i,x_j)=0 \bmod 3, \deg{f_i}=2$. Modulo $2$ can be ...

In an answer here Dima Pasechnik showed that constraints of the form $x_i x_j + a_{ij}x_i + b_{ij}x_j + c_{ij}$ are efficiently solvable modulo $2$ using Groebner basis. In comments he suggested that ...