Efficient Timed Reachability Analysis using Clock Difference Diagrams

Gerd Behrmann
Kim G. Larsen
Justin Pearson
Carsten Weise
Wang Yi

December 1998


One of the major problems in applying automatic verification tools to industrial-size systems is the excessive amount of memory required during the state-space exploration of a model. In the setting of real-time, this problem of state-explosion requires extra attention as information must be kept not only on the discrete control structure but also on the values of continuous clock variables.

In this paper, we present Clock Difference Diagrams, CDD's, a BDD-like data-structure for representing and effectively manipulating certain non-convex subsets of the Euclidean space, notably those encountered during verification of timed automata.

A version of the real-time verification tool UPPAAL using CDD's as a compact data-structure for storing explored symbolic states has been implemented. Our experimental results demonstrate significant space-savings: for 8 industrial examples, the savings are between 46% and 99% with moderate increase in runtime.

We further report on how the symbolic state-space exploration itself may be carried out using CDD's

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