Open AccessJournal Article
Durations, parametric model-checking in timed automata with presburger arithmetic
TLDR
In this article, the problem of model-checking a parametric extension of the logic TCTL over timed automata and establishing its decidability was considered, and it was shown that the set of durations of runs starting from a region and ending in another region is definable in the arithmetic of Presburger or in the theory of the reals.Abstract:
We consider the problem of model-checking a parametric extension of the logic TCTL over timed automata and establish its decidability. Given a timed automaton, we show that the set of durations of runs starting from a region and ending in another region is definable in the arithmetic of Presburger (when the time domain is discrete) or in the theory of the reals (when the time domain is dense). With this logical definition, we show that the parametric model-checking problem for the logic TCTL can easily be solved. More generally, we are able to effectively characterize the values of the parameters that satisfy the parametric TCTL formula.read more
Citations
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An automata-theoretic approach to constraint LTL
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Decision problems for lower/upper bound parametric timed automata
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Robust parametric reachability for timed automata
TL;DR: It is shown that the undecidability of parametric timed automata does not follow from their ability to specify punctual constraints in a dense time domain.
DissertationDOI
Diagnosis, Synthesis and Analysis of Probabilistic Models
TL;DR: In this article, the authors considered three important aspects of model checking Markov models: diagnosis, synthesis and analysis, and concluded that the three aspects are relatively independent while all contribute to developing new theory and algorithms in the field of probabilistic model checking.
Book ChapterDOI
An Automata-Theoretic Approach to Constraint LTL
Stéphane Demri,Deepak D'Souza +1 more
TL;DR: A new automata-theoretic technique is used to show pspace decidability of the logic for the constraint systems of linear-time temporal logic with constraints interpreted over a concrete domain.
References
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Rajeev Alur,David L. Dill +1 more
TL;DR: Alur et al. as discussed by the authors proposed timed automata to model the behavior of real-time systems over time, and showed that the universality problem and the language inclusion problem are solvable only for the deterministic automata: both problems are undecidable (II i-hard) in the non-deterministic case and PSPACE-complete in deterministic case.
Proceedings ArticleDOI
Model-checking for real-time systems
TL;DR: An algorithm is developed for model checking, that is, for determining the truth of a TCTL formula with respect to a timed graph, and it is argued that choosing a dense domain, instead of a discrete domain, to model time does not blow up the complexity of the model-checking problem.
Proceedings ArticleDOI
Parametric real-time reasoning
TL;DR: This work addresses the more realistic and more ambitious problem of deriving symbolic constraints on the timing properties required of real-time systems by introducing parametric timed automata whose transitions are constrained with parametric timing requirements.
Book
The computational complexity of logical theories
TL;DR: A lower bound on the theories of pairing functions and some additional lower bounds are given in this article, along with a technique for writing short formulas for defining complicated properties of complicated properties.
Proceedings ArticleDOI
Mixed real-integer linear quantifier elimination
TL;DR: The elementary theory of reals in varations of this langtmge in view of quantifier elimination and decidability is considered and positive and ncgat,ive results for various variaIlt lauguages are provided.