Clock Restriction Diagram: Yet Another Data-Structure for Fully Symbolic Veri cation of Timed Automata

Modern model-checkers for real-time systems are usually built around symbolic manipulation procedures of zones, which mean behavior-equivalent dense-time state subspaces and are represented by sets of clock di erence constraints. We propose CRD (Clock Restriction Diagram), which is a BDD-like data-structure for recording sets of zones, with related set-oriented operations for fully symbolic veri cation of realt-time systems. CRD with zones in reduced form (or reduced CRD in short), which contains minimal number of clock inequalities to characterize a zone, are de ned and can be used as a canonical representation for state space. Reduced CRD is more space-eÆcient than former proposal like DBM, NDD, CDD, and RED. We develop an algorithm that converts given CRDs to reduced CRDs without rst computing its closure form (which records the shortest path distance between every pair of clocks) in some representations. We implemented CRD in a new version of our veri er red for timed automata and compare its performance with Kronos's and UPPAAL's against several benchmarks.