# Language Emptiness of Continuous-Time Parametric Timed Automata

@inproceedings{Benes2015LanguageEO, title={Language Emptiness of Continuous-Time Parametric Timed Automata}, author={Nikola Benes and Peter Bezdek and Kim Guldstrand Larsen and Jir{\'i} Srba}, booktitle={International Colloquium on Automata, Languages and Programming}, year={2015} }

Parametric timed automata extend the standard timed automata with the possibility to use parameters in the clock guards. In general, if the parameters are real-valued, the problem of language emptiness of such automata is undecidable even for various restricted subclasses. We thus focus on the case where parameters are assumed to be integer-valued, while the time still remains continuous. On the one hand, we show that the problem remains undecidable for parametric timed automata with three…

## 47 Citations

### Reachability in two-parametric timed automata with one parameter is EXPSPACE-complete

- Mathematics, Computer ScienceSTACS
- 2021

The main result is that the reachability problem for two-parametric timed automata with one parameter is EXPSPACE-complete, and a series of techniques to partition a fictitious run of a POCA into several carefully chosen subruns that allow us to prove that it is sufficient to consider a parameter value of exponential magnitude only.

### Timed Automata with Parametric Updates

- Mathematics2018 18th International Conference on Application of Concurrency to System Design (ACSD)
- 2018

While the EF-emptiness problem is undecidable for rational-valued parameters, it becomes PSPACE-complete for integer-valuedparametric extensions and exact synthesis of the parameter valuations set can be achieved.

### 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.

### 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.

### 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.

### 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.

### On the Expressiveness of Parametric Timed Automata

- Computer ScienceFORMATS
- 2016

Two definitions for the expressiveness of parametric timed models are proposed: the first in terms of all the untimed words that can be generated for all possible valuations of the parameters, the second with the additional information of which parameter valuations allow which word, thus more suitable for synthesis issues.

### Liveness in L/U-Parametric Timed Automata

- Computer Science, Mathematics2017 17th International Conference on Application of Concurrency to System Design (ACSD)
- 2017

This work proves that: (1) the existence of at least one parameter valuation for which there exists an infinite run in the automaton is PSPACE-complete, and (2) theexistence of a parameter valuation such that the system has a deadlock is however undecidable.

### Distributed parametric model checking timed automata under non-Zenoness assumption

- Computer ScienceFormal Methods in System Design
- 2021

This work shows that the emptiness of the set of parameter valuations for which at least one counterexample run being non-Zeno is undecidable for PTAs, and proposes a procedure based on a transformation of PTAs into Clock Upper Bound PTAs to derive all valuations whenever it terminates, and some of them otherwise.

### Context-free timed formalisms: Robust automata and linear temporal logics

- Computer ScienceInf. Comput.
- 2022

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