Probabilistic and Topological Semantics for Timed Automata

@inproceedings{Baier2007ProbabilisticAT,
  title={Probabilistic and Topological Semantics for Timed Automata},
  author={Christel Baier and Nathalie Bertrand and Patricia Bouyer and Thomas Brihaye and Marcus Gr{\"o}{\ss}er},
  booktitle={FSTTCS},
  year={2007}
}
Like most models used in model-checking, timed automata are an idealized mathematical model used for representing systems with strong timing requirements. In such mathematical models, properties can be violated, due to unlikely (sequences of) events. We propose two new semantics for the satisfaction of LTL formulas, one based on probabilities, and the other one based on topology, to rule out these sequences. We prove that the two semantics are equivalent and lead to a PSPACE-Complete model… 
A Probabilistic Semantics for Timed Automata
TLDR
Two relaxed semantics for LTL over infinite runs of timed automata which rule out unlikely sequences of events are defined and it is proved that the probabilistic non-Zenoness can be decided for single-clock timing automata in NLOGSPACE.
Almost-Sure Model Checking of Infinite Paths in One-Clock Timed Automata
TLDR
Two relaxed semantics for LTL over infinite runs of timed automata which rule out unlikely sequences of events are defined and it is proved that the probabilistic non-Zenoness can be decided for single-clocktimed automata in NLOGSPACE.
Quantitative Model-Checking of One-Clock Timed Automata under Probabilistic Semantics
TLDR
This paper aims at computing the exact probability that a given timed automaton satisfies an omega-regular property, and develops a framework in which to compute a closed-form expression for this probability; it is proved that the threshold problem can be decided in that framework.
Robust Analysis of Timed Automata via Channel Machines
TLDR
A new encoding of the modified semantics of timed automata as a network of timed systems is proposed, and it is proved that robust model-checking for coFlat-MTL, a large fragment of MTL, is EXPSPACE-Complete.
Quantitative Robustness Analysis of Flat Timed Automata
TLDR
This work presents a symbolic algorithm for the computation of the parametric reachability set under this semantics for flat timed automata, and can compute the largest value of the parameter for a timed automaton to be safe.
Almost-Sure Model-Checking of Reactive Timed Automata
TLDR
This paper describes the subclass of reactive timed automata, a model in which both delays and discrete choices are made probabilistically, and proves decidability of the almost-sure model-checking problem under that restriction.
Timed Automata Can Always Be Made Implementable
TLDR
This work proposes a construction which makes timed automata implementable in the above sense, and builds a timed automaton A′ that exhibits the same behaviour as A, and moreover A′ is both robust and samplable by construction.
Untimed Language Preservation in Timed Systems
TLDR
A stronger notion of robustness is studied: it is shown how to decide whether the untimed language of a timed automaton is preserved under small enough imprecisions, and provide a bound on the imprecision parameter.
Statistical Model Checking for Networks of Priced Timed Automata
TLDR
The semantics provides the basis for satisfaction of probabilistic Weighted CTL properties (PWCTL), conservatively extending the classical satisfaction of timed automata with respect to TCTL, and offers an extension that allows to efficiently compare performance properties of NPTAs in a parametric setting.
Computing Maximum Reachability Probabilities in Markovian Timed Automata
TLDR
A novel stochastic extension of timed automata, i.e. Markovian Timed Automata (MTA), and shows that in the single-clock case, the problem can be reduced to solving a system of linear equations, whose coefficients are the time-bounded reachability probabilities in CTMDPs.
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References

SHOWING 1-10 OF 27 REFERENCES
Model-Checking for Probabilistic Real-Time Systems (Extended Abstract)
TLDR
This paper extends model-checking to stochastic real-time systems, whose behavior depends on probabilistic choice and quantitative time, with a model that can express constraints like “the delay between the request and the response is distributed uniformly between 2 to 4 seconds”.
Robust Model-Checking of Linear-Time Properties in Timed Automata
TLDR
The notion of implementability is extended to the broader class of linear-time properties, and PSPSACE algorithms are provided for the robust model-checking of Buchi-like and LTL properties and it is shown how those algorithms can be adapted in order to verify bounded-response- time properties.
Robustness and Implementability of Timed Automata
TLDR
This paper shows that this question of existence of a strictly positive value for the parameter Δ is closely related to a notion of robustness for timed automata defined in [Pur98] and proves that the implementability problem is decidable.
Model Checking for Probabilistic Timed Systems
  • J. Sproston
  • Computer Science
    Validation of Stochastic Systems
  • 2004
TLDR
Analysis of formally probabilistic timed systems using the technique of model checking, in which it is verified automatically whether a system satisfies a certain desired property, is considered.
Verifying Automata Specifications of Probabilistic Real-time Systems
We present a model-checking algorithm for a system presented as a generalized semi-Markov process and a specification given as a deterministic timed automaton. This leads to a method for automatic
Perturbed Timed Automata
TLDR
It is proved that determinization and decidability of language inclusion are not possible for multi-clock automata, even with perturbation, and that the perturbed language of a timed automaton with a single clock can be captured by a deterministic timed automation.
A Theory of Timed Automata
Dynamical Properties of Timed Automata
  • A. Puri
  • Computer Science
    Discret. Event Dyn. Syst.
  • 2000
TLDR
It is shown that the standard approach for performing reachability analysis is not correct when the clocks drift even by a very small amount, and an algorithm for computing R*(T,Z0) is presented and shown to be robust with respect to various types of modeling errors.
Validation of Stochastic Systems
TLDR
An overview of existing types of probabilistic systems and the relationship between these models is provided, and the existence of mappings between the corresponding system types that preserve and reflect bisimilarity is explained.
...
...