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

TL;DR

This paper introduces time-darts, a new data structure for symbolic state-space representation in timed automata, offering linear-time operations and better scalability than traditional discretization methods.

Contribution

The paper presents time-darts, a novel data structure that efficiently represents large state sets in timed automata with linear-time complexity operations.

Findings

Time-darts outperform complete discretization in experiments.

Time-darts scale better for models with larger constants.

The reachability algorithm for time-darts is proven correct.

Abstract

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.