Shooting problems P-23,P-25 via "Calculus of basic predicates" by E.A.Mironchick 2017

  That is a fairly strong demonstration of power and flexibility of "Calculus of basic predicates" approach by E.A.Mironchick 2017

In general we follow guidelines of technique developed in
http://kpolyakov.spb.ru/download/mea18bit.pdf

Per link mentioned above (quoting Helen A. Mironchick)
Let Et (x) be a predicate whose truth set is all x for which x & t ≠ 0.
If t is a power of two, then such a predicate will be called basic.
The basic predicate describes (fixes) a single unit in the binary notation.
Further, for brevity, the predicate Et (x) will be denoted by E(t);
we will also denote the truth set of this predicate.
(quoting ends)

Length of Biwise2 code

  

 Length of "Calculus of basic predicates" code

 (( E(A)*¬E(12) => (¬E(A)*E(21)) + ¬E(21)*¬E(12) ≡ 1
¬E(A) + E(12) + ¬E(A)*E(21) + ¬E(21)*¬E(12) ≡ 1
¬E(A) + E(12) + ¬E(21)*¬E(12) ≡ 1
¬E(A) + E(12) + ¬E(21) ≡ 1

Thus  А(max) =12

Length of Biwise2 code for ( x & 125 != 1) + ((x & 34 = 2) => (x & A = 0)) ≡ 1

 Length of "Calculus of basic predicates" code
 for    ( x & 125 != 1) + ((x & 34 = 2) => (x & A = 0))

E(124) + ¬E(1) + E(32) + ¬E(2) + ¬E(A) ≡ 1

So A(max) = 124

E(124) = E(64) + E(32) + E(16) + E(8) + E(4)
E(64) + E(32) + E(16) + E(8) + E(4) +
      + ¬E(1) + E(32) + ¬E(2) + ¬E(A) ≡ 1

So A(min) = 4