Clock Difference Diagrams

In this paper, we present Clock Difference Diagrams (CDD), a new BDD-like data-structure for effective representation and manipulation of certain non-convex subsets of the Euclidean space, notably those encountered in verification of timed automata. It is shown that all set-theoretic operations including inclusion checking may be carried out efficiently on Clock Difference Diagrams. Other clock operations needed for fully symbolic analysis of timed automata e.g. future- and reset-operations, can be obtained based on a so-called tight normalform for CDD. A version of the real-time verification tool UPPAAL using Clock Difference Diagrams as the main data-structure has been implemented. Experimental results demonstrate significant space-savings: for nine industrial examples the savings are in average 42% with moderate increase in runtime.