# On the expressive power of invariants in parametric timed automata

## TL;DR

This paper introduces a syntactic restriction on parametric timed automata that preserves expressiveness while enabling decidable parameter synthesis, offering a practical trade-off between complexity and expressiveness.

## Contribution

It proposes a new subclass of PTAs with only invariants, allowing exact parameter synthesis under certain constraints, balancing expressiveness and decidability.

## Key findings

- Decidability of reachability in the new formalism.
- Exact synthesis of parameter valuations for reachability.
- Applicability demonstrated through a case study.

## Abstract

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 consisting in removing guards (constraints on transitions) to keep only invariants (constraints on locations). While this restriction preserves the expressiveness of PTAs (and therefore their undecidability), an additional restriction on the type of constraints allows to not only prove decidability, but also to perform the exact synthesis of parameter valuations satisfying reachability. This formalism, that seems trivial at first sight as it benefits from the decidability of the reachability problem with a better complexity than Timed Automata (TAs), suffers from the undecidability of the whole TCTL logic that TAs, on the contrary enjoy. We believe our formalism allows for an interesting trade-off between decidability and practical expressiveness and is therefore promising. We show its applicability in a small case study.