What's Decidable About Parametric Timed Automata?

@inproceedings{Andr2015WhatsDA,
  title={What's Decidable About Parametric Timed Automata?},
  author={{\'E}tienne Andr{\'e}},
  booktitle={FTSCS},
  year={2015}
}
  • É. André
  • Published in FTSCS 6 November 2015
  • Computer Science
Parametric timed automata (PTA) are a powerful formalism to reason, simulate and formally verify critical real-time systems. After two decades of research on PTA, it is now well-understood that any non-trivial problem studied is undecidable for general PTA. We provide here a survey of decision and computation problems for PTA. On the one hand, bounding time, bounding the number of parameters or the domain of the parameters does not (in general) lead to any decidability. On the other hand… 

What’s decidable about parametric timed automata?

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References

SHOWING 1-10 OF 35 REFERENCES

Decision Problems for Parametric Timed Automata

TLDR
This paper exhibits a subclass of PTAs with bounded rational-valued parameters for which the parametric reachability emptiness problem is decidable, and presents further results improving the boundary between decidability and undecidability for PTAs and their subclasses.

Linear parametric model checking of timed automata

Language Emptiness of Continuous-Time Parametric Timed Automata

TLDR
This work shows that the parametric language emptiness is decidable for parametric timed automata with three clocks and one parameter, the first positive result in the case of continuous-time and unbounded integer parameters.

Integer Parameter Synthesis for Timed Automata

TLDR
This work provides a subclass of parametric timed automata (PTA) that it is argued that it retains most of the practical usefulness of PTA, and shows that the problem of the existence of parameter values such that some TCTL property is satisfied is PSPACE-complete.

Integer Parameter Synthesis for Real-Time Systems

TLDR
This work provides a subclass of parametric timed automata (PTA) that it is argued that it retains most of the practical usefulness of PTA for the modeling of real-time systems and shows that the problem of the existence of parameter values such that some TCTL property is satisfied is PSPACE-complete.

MTL-Model Checking of One-Clock Parametric Timed Automata is Undecidable

TLDR
It is proved that MTL-model checking for parametric timed automata is undecidable, even if the automaton uses only one clock and one parameter and is deterministic.

Parametric real-time reasoning

TLDR
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.

Bounded Model Checking for Parametric Timed Automata

TLDR
This paper shows how bounded model checking can be applied to parameter synthesis for parametric timed automata with continuous time, and presents an implementation for the existential part of CTL−X.

Decidability and Complexity Results for Timed Automata and Semi-linear Hybrid Automata

TLDR
It is shown that the existence of a Zeno run is Σ11 -complete for semi-linear hybrid automata; it is too complex to be expressed in first-order arithmetic.

Integer-Complete Synthesis for Bounded Parametric Timed Automata

TLDR
This paper introduces a parametric extrapolation, that allows an underapproximation in the form of linear constraints containing all the integer points ensuring reachability or unavoidability, and all the (non-necessarily integer) convex combinations of these integer points, for general PTA with a bounded parameter domain.