Weak morphisms of higher dimensional automata

We introduce weak morphisms of higher dimensional automata and use them to define preorder relations for HDAs, among which are homeomorphic abstraction and trace equivalent abstraction. It is shown that homeomorphic abstraction is essentially always stronger than trace equivalent abstraction. We also define the trace language of an HDA and show that, for a large class of HDAs, it is invariant under trace equivalent abstraction. (C) 2014 Elsevier B.V. All rights reserved.