Unleash the full power of the Mapping Method (Graphs and Systems of Boolean Equations by E.A. Mironchik)

Consider foillowing system

Why I believe it's worth to analyze ? Original task ( just xj,yj,zj in every bracket)  may be solved in a couple of minutes just scanning through {X} bitmask table and calculating sum of solutions  for each row of {X}. Four variables in brackets result  bitmask approach failure to generate simple (y,z) systems for each row in {X}. Thus it clearly demonstrates an advantage of "Graph&&Mapping method"  idea by Helen Mironchick

(x1=>x2)^(x2=>x3)^(x3=>x4)^(x4=>x5)=1

((¬x1^y1^z1^w1) v (x1^¬y1^z1^w1) v (x1^y1^¬z1^w1) v (x1^y1^z1^¬w1)) =1

((¬x2^y2^z2^w2) v (x2^¬y2^z2^w2) v (x2^y2^¬z2^w2) v (x2^y2^z2^¬w2)) =1

((¬x3^y3^z3^w3) v (x3^¬y3^z3^w3) v (x3^y3^¬z3^w3) v (x3^y3^z3^¬w3)) =1

((¬x4^y4^z4^w4) v (x4^¬y4^z4^w4) v (x4^y4^¬z4^w4) v (x4^y4^z4^¬w4)) =1

((¬x5^y5^z5^w5) v (x5^¬y5^z5^w5) v (x5^y5^¬z5^w5) v (x5^y5^z5^¬w5)) =1

Convert system as follows

(x1=>x2)^((¬x1^y1^z1^w1) v (x1^¬y1^z1^w1) v (x1^y1^¬z1^w1) v (x1^y1^z1^¬w1)) =1

(x2=>x3)^((¬x2^y2^z2^w2) v (x2^¬y2^z2^w2) v (x2^y2^¬z2^w2) v (x2^y2^z2^¬w2)) =1

(x3=>x4)^((¬x3^y3^z3^w3) v (x3^¬y3^z3^w3) v (x3^y3^¬z3^w3) v (x3^y3^z3^¬w3)) =1

(x4=>x5)^((¬x4^y4^z4^w4) v (x4^¬y4^z4^w4) v (x4^y4^¬z4^w4) v (x4^y4^z4^¬w4)) =1

((¬x5^y5^z5^w5) v (x5^¬y5^z5^w5) v (x5^y5^¬z5^w5) v (x5^y5^z5^¬w5)) =1

Build complete graph for system

    Pass system via Polyakov's Control

 

References

1. http://kpolyakov.spb.ru/download/mea-2016-8.pdf