Certain Relations between Properties of Maps of Tessellation Automata

In a different approach, Hedlund [4], Sears [13], and Ryan [12] defined the shift dynamical system and investigated the properties of the continuous transformations which commute with the shift transformations, and showed many interesting results in one-dimensional tessellation spaces. Hedlund conjectured that in some sense, the set A of all parallel maps which are injective on the set C of all configurations is relatively sparse in the set E of all parallel maps which are surjective on C. Sears showed that A is nowhere dense in E under