  Parametric timed automata (PTA) extend timed automata with unknown constants
("parameters"), at the price of undecidability of most interesting problems.
The (untimed) language preservation problem ("given a parameter valuation, can
we find at least one other valuation with the same untimed language?") is
undecidable for PTAs. We prove that this problem remains undecidable for
parametric event-recording automata (PERAs), a subclass of PTAs that
considerably restrains the way the language can be used; we also show it
remains undecidable even for slightly different definitions of the language,
i.e., finite sequences of actions ending in or passing infinitely often through
accepting locations, or just all finite untimed words (without accepting
locations).
