# 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} }

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…

## 7 Citations

### 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.

### On the Expressive Power of Invariants in Parametric Timed Automata

- Computer Science2019 24th International Conference on Engineering of Complex Computer Systems (ICECCS)
- 2019

A syntactic restriction on PTAs consisting in removing guards to keep only invariants is proposed to allow for an interesting trade-off between decidability and practical expressiveness and is therefore promising.

### F L ] 1 2 Ju n 20 19 Consistency in Parametric Interval Probabilistic Timed Automata ∗

- Computer Science
- 2019

It is shown that the existence of timing parameter valuations ensuring consistency is undecidable in the general context, but still exhibit a syntactic condition on parameters to ensure decidability.

### Compositional Liveness-Preserving Conformance Testing of Timed I/O Automata - Technical Report

- Computer ScienceFACS
- 2019

An improved version of tioco is proposed, called live timed ioco (ltioco), tackling various weaknesses of existing definitions and extending the theory of zone graphs to enable ltioco testing on a finite semantic model of TIOA.

### Parametric Verification: An Introduction

- Computer ScienceTrans. Petri Nets Other Model. Concurr.
- 2019

This paper presents not only the basic formal concepts tackled in the video version, but also an extensive literature to provide the reader with further references covering the area, to introduce motivation behind parametric verification in general and focus on different models and approaches for verifying several kinds of systems.

### 1 J ul 2 01 9 Parametric Verification : An Introduction ⋆

- Computer Science
- 2019

This paper first introduces motivation behind parametric verification in general, and then focuses on different models and approaches, for verifying several kinds of systems, including Parametric Timed Automata, for modelling real-time systems, where the timing constraints are not necessarily known a priori.

## References

SHOWING 1-10 OF 35 REFERENCES

### 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.

### Linear parametric model checking of timed automata

- Computer Science, MathematicsJ. Log. Algebraic Methods Program.
- 2002

### 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.

### Integer Parameter Synthesis for Timed Automata

- Mathematics, Computer ScienceTACAS
- 2013

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

- 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.

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

- Computer ScienceSynCoP
- 2014

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

- Computer ScienceSTOC
- 1993

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

- Computer Science, MathematicsACSD/Petri Nets Workshops
- 2010

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

- 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.

### Integer-Complete Synthesis for Bounded Parametric Timed Automata

- Computer ScienceRP
- 2015

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.