Message Passing Algorithm for Solving QBF Using More Reasoning

Algorithm 2

EHSPQBF algorithm.

Procedure EHSPQBF (𝑄⋅𝐸)

(1) preprocess (𝑄⋅𝐸);

(2)  if (𝐸=Ø) then  return SAT;

(3)  if  𝐶_Ø∈𝐸 ∨ 𝐶_all∀∈𝐸  then  return UNSAT;

(4) result = deduce();

(5)  if (result = conflict)

(6)  then analyze_conflict();

(7)  if (result = satisfaction)

(8)  then analyze_satisfaction();

(9)  𝑣← SP_choosevariable (𝑄⋅𝐸);

(10)  if (𝑣 is existential)

(11)  then  return EHSPQBF (𝑄⋅𝐸|_𝑣=true) or EHSPQBF (𝑄⋅𝐸|_𝑣=false)

(12)  if (v is universal)

(13)  then  return EHSPQBF (𝑄⋅𝐸|_𝑣=true) and EHSPQBF (𝑄⋅𝐸|_𝑣=false)