Reflectiveness and compression of threshold transformations Original Research Article

A reflective transformation is a one-to-one Boolean transformation such that its inverse is isometrically similar to itself. Any Boolean isometry is proved to be reflective through some Boolean isometry of order 2. Some conditions for reflectiveness are given for the [ ]-representations of self-dual transformations introduced by the authorʹs previous paper. Next, a condition for a threshold transformation to be expansible is described. Then all currently known one-to-one minimal incompressible threshold transformations are shown to be reflective through some Boolean isometries of order 2.