Memory Efficient Data Structures for Explicit Verification of Timed Systems

Abstract

Abstract. Timed analysis of real-time systems can be performed using continuous (symbolic) or discrete (explicit) techniques. The explicit state-space exploration can be considerably faster for models with moderately small constants, however, at the expense of high memory consumption. In the setting of timed-arc Petri nets, we explore new data structures for lowering the used memory: PTries for efficient storing of configurations and time darts for semi-symbolic description of the statespace. Both methods are implemented as a part of the tool TAPAAL and the experiments document at least one order of magnitude of memory savings while preserving comparable verification times.

Interval Abstraction Refinement for Model Checking of Timed-Arc Petri Nets

“…The experiments, run on a Macbook Pro 2.7GHz Intel Core i7, were terminated once the memory usage exceeded 4GB (OOM) or the verification took longer than 5 minutes ( ). In the summary table we report on the running time using TAPAAL's discrete verification engine [18] and the column labelled with r = 1 corresponds to verification where no approximation is used. The rows marked with "no trace" correspond to EF or EG queries that are not satisfied (and hence no trace is returned).…”

“…This is caused by the fact that the continuous engine performs a symbolic exploration that is not that affected by the size of the constants like during the explicit exploration. The comparison of discrete vs. continuous verification is not in the scope of this paper and we refer to [6,21,18] for further discussion.…”

“…On the other hand, the discrete state-spaces can be searched in a direct manner where the clock values are remembered explicitly. The explicit approach can successfully compete with the symbolic one, as long as the constants in clock guards are reasonably small [6,21,19,3,18]. As the sizes of constants grow, the models become increasingly more difficult to verify, in particularly in case of explicit verification techniques.…”

“…The authors in [14] suggest an algorithm for under-and over-approximations of timed safety automata by approximating the union operation on zones. Our method is not based on zones and it is targeted instead towards explicit state- space exploration techniques where it can be combined with some recently introduced techniques and data structures like PTrie and Time Darts [18]. Finally, a time-relaxing method for a network of automata where events have intervaldurations is described in [2].…”

Optimal compression of combinatorial state spaces

“…BDDs [6] also store state vectors efficiently; however, Jensen et al [22] figure them too slow for state space exploration. The tool from [21] implements reachability with Tries for Petri nets.…”