Imagine I can specify a certain process as a Petri Net. Is there any good software, open source or not, that can verify my process against some conditions I declare (or code) in some language?
In case not, is there an open source software that does at least simulations?
It's not really a field I know much about, but I doubt it.
Model-checking problems get very hard (sometimes very undecidable) very fast. Whether what you ask is faisable at all depends on the kind of statements you are interested in checking and on what restrictions on the Petri nets structure you are willing to impose.
On general nets, all interesting questions (e.g. marking reachability) are $\text{EXPSPACE}$-hard. General model-checking is undecidable even for very weak branching-time temporal logics; several interesting fragments of linear-time logics are decidable but at least as hard as the reachability problem, i.e. $\text{EXPSPACE}$-hard.
Software recommendations are off-topic here, but I'm sure plenty of simulators are available online.
