I am trying to solve such system of boolean equations:
$b_{i}^{0}=\oplus_{j=0}^{i}a_{j}^{0} \land a_{i-j}^{1}, i\in[0..31] $
$b_{i}^{1}=\oplus_{j=0}^{30-i}a_{1 + i + j}^{0} \land a_{31 - j}^{1}, i\in[0..30]$
Note: $a_i^j$ - is unknown bit, $b_i^j$ is known bit value
I tried to solve such system with brute-force. It took approximately about 30 min. It is too slow for me, I want to get fast solution (~few seconds)