Connectivity-only synchronization for difference DFAs in ℝ^d

Determine whether every connected difference DFA in ℝ^d is synchronizable, removing the bidirectional connectedness assumption used to prove synchronization in Section 4.

Background

The paper proves that every bidirectional connected difference DFA in ℝ^d is synchronizable via the cornering strategy and convex-geometric arguments. It then raises the possibility of relaxing bidirectional connectedness to mere strong connectivity.

Establishing synchronization under connectivity alone would broaden the applicability of the cornering framework to more general geometric automata models relevant in robotics and game dynamics.