Time-Darts: A Data Structure for Verification of Closed Timed Automata

• Published in: Electronic proceedings in theoretical computer science Vol. 102; no. Proc. SSV 2012; pp. 141 - 155
• Main Authors: Jørgensen, Kenneth Y., Larsen, Kim G., Srba, Jiří
• Format: Journal Article
• Language: English
• Published: Open Publishing Association 26.11.2012
• ISSN: 2075-2180; 2075-2180
• DOI: 10.4204/EPTCS.102.13

Symbolic data structures for model checking timed systems have been subject to a significant research, with Difference Bound Matrices (DBMs) still being the preferred data structure in several mature verification tools. In comparison, discretization offers an easy alternative, with all operations having linear-time complexity in the number of clocks, and yet valid for a large class of closed systems. Unfortunately, fine-grained discretization causes itself a state-space explosion. We introduce a new data structure called time-darts for the symbolic representation of state-spaces of timed automata. Compared with the complete discretization, a single time-dart allows to represent an arbitrary large set of states, yet the time complexity of operations on time-darts remain linear in the number of clocks. We prove the correctness of the suggested reachability algorithm and perform several experiments in order to compare the performance of time-darts and the complete discretization. The main conclusion is that in all our experiments the time-dart method outperforms the complete discretization and it scales significantly better for models with larger constants.