**Input**: System of $\Omega(t)$ independent polynomials in $\mathbb F\_2[x\_1,\dots,x\_{t}]$ of degree $O(t)$.


1. Can we output a common solution of the system in polynomial time?
2. Can we output parity of the number of common solutions of the system in polynomial time?



On a system of equations in $\mathbb F_2$
1 - No, the problem is NP-hard even if degree of all polynomials is 2.


2 - See, for example, paper [Solving Systems of Polynomial Equations over
GF(2) by a Parity-Counting Self-Reduction](https://acris.aalto.fi/ws/portalfiles/portal/35681013/LIPIcs_ICALP_2019_26.pdf) by Björklund et al.


