Finding Best and Worst Case Execution Times of Systems Using Difference-Bound Matrices

Al-Bataineh, Omar I.; Reynolds, Mark; French, Tim

doi:10.1007/978-3-319-10512-3_4

Cited by 3 publications

(9 citation statements)

References 15 publications

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“…Zones are represented as sets of clock constraints, UC denotes the set of constraints involving the global clock x i . Thus, Z \ UC denotes the zone Z where constraints on x i are ignored (though this is not formally defined in [ARF14]).…”

Section: A a Counter-example To The Algorithm Of [Arf14]mentioning

confidence: 99%

“…However the paper does not mention any assumptions regarding the order of exploration that would invalidate our counter-example. We contacted the authors of [ARF14], asking to get access to the prototype implementation mentioned in the paper, but did not get an answer.…”

Section: A a Counter-example To The Algorithm Of [Arf14]mentioning

confidence: 99%

“…Algorithm 2 is the algorithm proposed in [ARF14] to compute optimal-time reachability in timed automata. Briefly, the approach considers a global clock, denoted by x i , to measure the duration of the current run.…”

Section: A a Counter-example To The Algorithm Of [Arf14]mentioning

confidence: 99%

“…Several tools propose WCET analysis based on timed automata: TIMES [AFM + 03] uses binary-search to evaluate WCET, while Uppaal [GELP10] and METAMOC [DOT + 10] rely on the algorithm of [RLS06] mentioned above; in particular they require bounded clocks to ensure termination. A tentative workaround to this problem has been proposed in [ARF14], but we are uncertain about its correctness (as we explain with a counter-example in Appendix A).…”

Section: Introductionmentioning

confidence: 99%

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Symbolic Optimal Reachability in Weighted Timed Automata

Bouyer

Colange

Markey

2016

Computer Aided Verification

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Weighted timed automata have been defined in the early 2000's for modelling resource-consumption or -allocation problems in real-time systems. Optimal reachability is decidable in weighted timed automata, and a symbolic forward algorithm has been developed to solve that problem. This algorithm uses so-called priced zones, an extension of standard zones with cost functions. In order to ensure termination, the algorithm requires clocks to be bounded. For unpriced timed automata, much work has been done to develop sound abstractions adapted to the forward exploration of timed automata, ensuring termination of the model-checking algorithm without bounding the clocks. In this paper, we take advantage of recent developments on abstractions for timed automata, and propose an algorithm allowing for symbolic analysis of all weighted timed automata, without requiring bounded clocks.themselves. It can be seen as a priced counterpart of a recently-developed inclusion test over standard zones [HSW12]: it compares abstractions of zones without explicitly computing them, which has shown its efficiency for the analysis of timed automata. We prove that the forward-exploration algorithm using priced zones with this inclusion test indeed computes the optimal cost, and that it terminates. We also propose an algorithm to effectively decide inclusion of priced zones. We implemented our algorithm, and we compare it with that of [RLS06].Related work. The approach of [LBB + 01,RLS06] is the closest related work. Our algorithm applies to a more general class of systems (unbounded clocks), and always computes fewer symbolic states on bounded models (see Remark 1); also, while the inclusion test of [RLS06] reduces to a mincost flow problem, for which efficient algorithms exist, we had to develop specific algorithms for checking our new inclusion relation. We develop this comparison with [RLS06] further in Section 6, including experimental results.Our algorithm can be used in particular to compute best-and worst-case execution times. Several tools propose WCET analysis based on timed automata: TIMES [AFM + 03] uses binary-search to evaluate WCET, while Uppaal [GELP10] and METAMOC [DOT + 10] rely on the algorithm of [RLS06] mentioned above; in particular they require bounded clocks to ensure termination. A tentative workaround to this problem has been proposed in [ARF14], but we are uncertain about its correctness (as we explain with a counter-example in Appendix A).By lack of space, all proofs are given in a separate appendix.

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Section: A a Counter-example To The Algorithm Of [Arf14]mentioning

confidence: 99%

Section: A a Counter-example To The Algorithm Of [Arf14]mentioning

confidence: 99%

Section: A a Counter-example To The Algorithm Of [Arf14]mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Symbolic Optimal Reachability in Weighted Timed Automata

Bouyer

Colange

Markey

2016

Computer Aided Verification

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“…The proposed solution allows one to compute the WCET of TA in only one run of the zone construction instead of making repeated guesses (guided by binary search) and multiple model checking queries as done in [Met04]. However, in [ABRF14] we limit applicability of our solution to timed automata without infinite cycles. In the present paper, we give a more general solution to the problem that can work on any arbitrary diagonal-free TA 1 including those containing infinite cycles.…”

Section: Introductionmentioning

confidence: 99%

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

Al-Bataineh

Reynolds

French

2017

Theoretical Computer Science

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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.

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Accelerating worst case execution time analysis of timed automata models with cyclic behaviour

2015

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The paper presents a new efficient algorithm for computing worst case execution time (WCET) of systems modelled as timed automata (TA). The algorithm uses a set of abstraction techniques that improve significantly the efficiency of WCET analysis of TA models with cyclic behaviour. We show that the proposed abstractions are exact with respect to the WCET problem in the sense that the WCET computed in the abstract model is equal to the one computed in the concrete model. We also compare our algorithm with the one implemented in the model checker UPPAAL which shows that when infinite cycles exist (i.e. cycles that can be run infinitely often), UPPAAL’s algorithm may not terminate, and when largely repetitive finite cycles exist (i.e. cycles that can be run a large number of times but finite), UPPAAL’s algorithm suffers from the state space explosion, thus leading to a low efficiency or resource exhaustion.

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Finding Best and Worst Case Execution Times of Systems Using Difference-Bound Matrices

Cited by 3 publications

References 15 publications

Symbolic Optimal Reachability in Weighted Timed Automata

Symbolic Optimal Reachability in Weighted Timed Automata

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

Accelerating worst case execution time analysis of timed automata models with cyclic behaviour

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