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Minimal domain

SYNTAX: Notion in checking theory. The minimal domain of X is the smallest subset K of the domain(X) S, such that for any element A of S, some element B of K reflexively dominates A. EXAMPLE: In (i), the minimal domain of X is {UP, ZP, WP, YP, H}. The minimal domain of H is {UP, ZP, WP, YP}.

(i)    XP1
       /\
      /  \
     UP  XP2
        /\
       /  \
     ZP1    X'
    /\      /\
   /  \    /  \
  WP  ZP2  X1  YP
          /\
         /  \
        H   X2