Finding minimum and maximum termination time of timed automata models with cyclic behaviour

Abstract

The paper presents a novel algorithm for computing worst case execution time (WCET) or maximum termination time of real-time systems using the timed automata (TA) model checking technology. The algorithm can work on any arbitrary diagonal-free TA and can handle more cases than previously existing algorithms for WCET computation, as it can handle cycles in TA and decide whether they lead to an infinite WCET. We show soundness of the proposed algorithm and study its complexity. To our knowledge, this is the first model checking algorithm that addresses comprehensively the WCET problem of systems with cyclic behaviour. In [BFH + 01] Behrmann et al provide an algorithm for computing the minimum cost/time of reaching a goal state in priced timed automata (PTA). The algorithm has been implemented in the well-known model checking tool UPPAAL to compute the minimum time for termination of an automaton. However, we show that in certain circumstances, when infinite cycles exist, the algorithm implemented in UPPAAL may not terminate, and we provide examples which UPPAAL fails to verify.

Secure Information Release in Timed Automata

“…There has been a lot of research [3,4] done for determining the maximum (max t ) or minimum (min t ) execution time that an automaton needs to move from a location q s to a location q t . One possibility is to make use of this work [3,4] and thus the predicate Φ q would amount to checking if the execution time between the two nodes of interest (q and ipd Y (q)) is constant (e.g. max t = min t ).…”

A Comparative Study of Decision Diagrams for Real-Time Model Checking

“…In the last two decades, there has been a considerable development in the extrapolation procedure for TA for the purpose of providing coarser abstractions of TA [10,14,8]. We refer the reader to [1] for more details about di↵erent kinds of extrapolation techniques.…”

Computing Maximal Expected Termination Time of Probabilistic Timed Automata

“…The WCET problem for the case of non-probabilistic timed systems with cyclic behavior has been addressed in [2], where a model checking algorithm based on the zone-abstraction technique was used allowing on-the-fly computation of WCET for timed automata models and detection of the cases where WCET may be unbounded. For probabilistic timed systems, for example, the problem becomes much harder, as any solution needs to handle both timed transitions and probability distributions simultaneously.…”

“…In [2], the authors proposed a model checking algorithm based on the zone abstraction for the problem of computing maximum termination time of non-probabilistic timed automata (TA). However, for probabilistic timed systems the problem may be much harder, as the solution needs to handle both timed transitions and probability distributions.…”

“…However, for probabilistic timed systems the problem may be much harder, as the solution needs to handle both timed transitions and probability distributions. Moreover, the abstractions, optimisations, and accelerations developed for the verification of WCET of TAs [1,2] cannot be used to verify expected WCET of PTAs, as cycles in PTAs exhibit both timing and probabilistic behavior.…”