# On the Expressive Power of Invariants in Parametric Timed Automata

@article{Andr2019OnTE, title={On the Expressive Power of Invariants in Parametric Timed Automata}, author={{\'E}tienne Andr{\'e} and Didier Lime and Mathias Ramparison}, journal={2019 24th International Conference on Engineering of Complex Computer Systems (ICECCS)}, year={2019}, pages={87-96} }

The verification of systems combining hard timing constraints with concurrency is challenging. This challenge becomes even harder when some timing constants are missing or unknown. Parametric timed formalisms, such as parametric timed automata (PTAs), tackle the synthesis of such timing constants (seen as parameters) for which a property holds. Such formalisms are highly expressive, but also undecidable, and few decidable subclasses were proposed. We propose here a syntactic restriction on PTAs…

## References

SHOWING 1-10 OF 18 REFERENCES

### What’s decidable about parametric timed automata?

- Computer ScienceInternational Journal on Software Tools for Technology Transfer
- 2017

A survey of decision and computation problems for PTAs, including formalisms close to parametric timed automata (such as parametric hybrid automata or parametric interrupt timedAutomata), and tools dedicated to PTAs and their extensions are studied.

### TCTL Model Checking Lower/Upper-Bound Parametric Timed Automata Without Invariants

- Computer Science, MathematicsFORMATS
- 2018

It is proved that without invariants, flat TCTL is decidable for L/U-PTAs by resolving the last non investigated liveness properties.

### Language Emptiness of Continuous-Time Parametric Timed Automata

- Computer Science, MathematicsICALP
- 2015

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.

### Decision Problems for Parametric Timed Automata

- Computer Science, MathematicsICFEM
- 2016

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.

### Integer Parameter Synthesis for Real-Time Systems

- Mathematics, Computer ScienceIEEE Transactions on Software Engineering
- 2015

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.

### Parametric updates in parametric timed automata

- Computer Science, MathematicsFORTE
- 2019

This work introduces a new class of Parametric Timed Automata (PTAs) where clocks are allowed to be compared to parameters in guards, as in classic PTAs, but also to be updated to parameters.

### Model-Checking in Dense Real-time

- Computer ScienceInf. Comput.
- 1993

An algorithm for model-checking, for determining the truth of a TCTL-formula with respect to a timed graph, is developed and it is argued that choosing a dense domain instead of a discrete domain to model time does not significantly blow up the complexity of the model- checking problem.

### Decision problems for lower/upper bound parametric timed automata

- Computer Science, MathematicsFormal Methods Syst. Des.
- 2007

It is shown that basic decision problems, such as emptiness, finiteness and universality of the set of parameter valuations for which there is a corresponding infinite accepting run of the automaton, is Pspace-complete.

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

- Computer Science, MathematicsHSCC
- 2000

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.