  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.
