A Symbolic Algorithm for the Analysis of Robust Timed Automata

Abstract

Abstract. We propose an algorithm for the analysis of robustness of timed automata, that is, the correctness of a model in the presence of small drifts of the clocks. The algorithm is an extension of the regionbased algorithm of Puri and uses the idea of stable zones as introduced by Daws and Kordy. Similarly to the assumptions made by Puri, we restrict our analysis to the class of timed automata with closed guards, progress cycles, and bounded clocks. We have implemented the algorithm and applied it to several benchmark specifications. The algorithm is a depth-first search based on on-the-fly reachability using zones.

Symbolic Quantitative Robustness Analysis of Timed Automata

“…org, and have been considered in [21], with the exception of the scheduling tests (Sched *) which were constructed from the experiments of [17]. We implemented Alg.…”

“…ulb.ac.be/di/verif/sankur). We consider two other competing algorithms: the first one is the recently published tool Verifix [21] which solves the infinitesimal robust safety problem but does not output any bound on δ. The second algorithm is our implementation of a binary search on the values of δ which iteratively calls an exact model checker until a given precision is reached.…”

“…Table 2 shows the performance of the binary search for varying precision ∈ { Table 1. Comparison between Symrob (breadth-first search, instantiated with K0 = 10) and Verifix [21]. The running time of the exact model checking implemented in Symrob is given for reference in the column "Exact" (the specification was satisfied without enlargement in all models).…”

“…We ran experiments to evaluate the performance of our procedure. Compared to [21], ours terminated faster in most cases, and sometimes with several orders of magnitude. To truly evaluate the gain of a parametric analysis, we also compared with a binary search on the values of δ using an exact model checker.…”

“…The flatness is a rather restrictive hypothesis since, for instance, it is easily violated when the system is obtained by composition of timed automata that contain cycles. Recently, a zone-based algorithm and a tool to solve Problem 1 for general timed automata was given [21]; but the algorithm does not compute any bound on δ. The latter algorithm is based, roughly, on extending the standard forward exploration of the state space augmented with the acceleration of all cycles encountered during the search, with some tricks to optimize the computations.…”