Verifying invariance properties of timed systems with duration variables

Bouajjani, Ahmed; Echahed, Rachid; Robbana, Riadh

doi:10.1007/3-540-58468-4_166

Cited by 17 publications

(15 citation statements)

References 12 publications

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“…Decidability of the reachability problem for CSHS has been studied in several works. In [BER94] it is shown that reachability in CSHS is decidable under the constraints that only nonstrict inequalities are used in edge guards, and timers are reset only at integer values. This result is based on a digitization technique which is a generalization of the digitization presented in [HMP92].…”

Section: Discussion and Related Workmentioning

confidence: 99%

Decidable Integration Graphs

Kesten

Pnueli

Sifakis

et al. 1999

Information and Computation

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Section: Discussion and Related Workmentioning

confidence: 99%

Decidable Integration Graphs

Kesten

Pnueli

Sifakis

et al. 1999

Information and Computation

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“…It has been shown that the reachability problem for multirate automata (a hybrid automaton where the variables run at any constant slope; see [34,35]) and rectangular automata [12,13] is decidable, under certain conditions. Some more decidability results were given for subclasses of linear hybrid systems, extended integrator graphs [36], and for timed graphs with one stopwatch [37].…”

Section: Related Workmentioning

confidence: 99%

Low dimensional hybrid systems – decidable, undecidable, donʼt know

Asarin

Mysore

Pnueli

et al. 2012

Information and Computation

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Even though many attempts have been made to define the boundary between decidable and undecidable hybrid systems, the affair is far from being resolved. More and more low dimensional systems are being shown to be undecidable with respect to reachability, and many open problems in between are being discovered. In this paper, we present various two dimensional hybrid systems for which the reachability problem is undecidable. We show their undecidability by simulating Minsky machines. Their proximity to the decidability frontier is understood by inspecting the most parsimonious constraints necessary to make reachability over these automata decidable. We also show that for other two dimensional systems, the reachability question remains unanswered, by proving that it is as hard as the reachability problem for piecewise affine maps on the real line, which is a well known open problem.

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“…Other work also deals with notions of robustness in order to guarantee that dense-time TA are implementable with non-ideal architectures [11]. Another well-known notion of discretization is the one based on the concept of digitization [22]; several authors have applied this quite general notion to the practical verification of descriptive [30,24,9,34] or operational [20,26,7,6,29,8,5,31,10] formalisms. See also the related work section of [16] for more references about discretization techniques.…”

Section: Related Workmentioning

confidence: 99%

Practical Automated Partial Verification of Multi-paradigm Real-Time Models

Furia

Pradella

Rossi

2008

Formal Methods and Software Engineering

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This article introduces a fully automated verification technique that permits to analyze real-time systems described using a continuous notion of time and a mixture of operational (i.e., automata-based) and descriptive (i.e., logic-based) formalisms. The technique relies on the reduction, under reasonable assumptions, of the continuous-time verification problem to its discrete-time counterpart. This reconciles in a viable and effective way the dense/discrete and operational/descriptive dichotomies that are often encountered in practice when it comes to specifying and analyzing complex critical systems. The article investigates the applicability of the technique through a significant example centered on a communication protocol. More precisely, concurrent runs of the protocol are formalized by parallel instances of a Timed Automaton, while the synchronization rules between these instances are specified through Metric Temporal Logic formulas, thus creating a multi-paradigm model. Verification tests run on this model using a bounded validity checker implementing the technique show consistent results and interesting performances.

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Verifying invariance properties of timed systems with duration variables

Cited by 17 publications

References 12 publications

Decidable Integration Graphs

Decidable Integration Graphs

Low dimensional hybrid systems – decidable, undecidable, donʼt know

Practical Automated Partial Verification of Multi-paradigm Real-Time Models

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