New Algorithms for Bidirectional Singleton Arc Consistency

Algorithm 5

Judge-DP (𝑋,𝐷_𝑋).

(1)  𝑄←𝑃;

(2)  𝐷^𝑄(𝑋)←𝐷_𝑋;

(3)  if  𝐷^𝑄(𝑋)=0 then return true;

(4)  if  𝜌(𝑄, 𝑋) = ⟂  then goto  𝐿;

(5)  if AC(𝑄) = ⟂ then goto  𝐿;

(6)  foreach (𝑌, 𝑏) ∈ 𝑄 s.t 𝑌≠𝑋 do

(7)   if AC (𝑃|_𝑌←𝑏)≠⟂  then

(8)    if exist 𝑎∈𝐷_𝑋 s.t. (𝑋,𝑎)∉  AC(𝑃|_𝑌=𝑏) then

(9)      𝑄←𝑄⧵{(𝑌,𝑏)};

(10)  if AC(𝑄) ≠ ⟂  then return true;

(11) L:

(12)  if  𝐷_𝑋=1  then

(13)     𝑃←𝑃⧵𝑋,𝐷_𝑋;

(14)     𝐶𝐻𝐴𝑁𝐺𝐸← true;

(15)     if  𝑃=⟂  then return ⟂;

(16)      else return true;

(17)  𝐷₁∶∶𝐷₂←𝐷_𝑋;

(18)  if Judge-DP(𝑋,𝐷₁)=⟂  ∥  Judge-DP(𝑋,𝐷₂) = ⟂  then return  ⟂;

(19)  return true;