Soundness of reset workflow nets

Workflow nets are a well-established variant of Petri nets for the modeling of process activities such as business processes. The standard correctness notion of workflow nets is soundness, which comes in several variants. Their decidability was shown decades ago, but their complexity was only identified recently. In this work, we are primarily interested in two popular variants: $1$-soundness and generalised soundness. Workflow nets have been extended with resets to model workflows that can, e.g., cancel actions. It has been known for a while that, for this extension, all variants of soundness, except possibly generalised soundness, are undecidable. We complete the picture by showing that generalised soundness is also undecidable for reset workflow nets. We then blur this undecidability landscape by identifying a property, coined ``$1$-in-between soundness'', which lies between $1$-soundness and generalised soundness. It reveals an unusual non-monotonic complexity behaviour: a decidable soundness property is in between two undecidable ones. This can be valuable in the algorithmic analysis of reset workflow nets, as our procedure yields an output of the form ``$1$-sound'' or ``not generalised sound'' which is always correct.