Abstract processes in the absence of conflicts in general place/transition systems

Goltz and Reisig generalised Petri's concept of processes of one-safe Petri nets to general nets where places carry multiple tokens. BD-processes are equivalence classes of Goltz-Reisig processes connected through the swapping transformation of Best and Devillers; they can be considered as an alternative representation of runs of nets. Here we present an order respecting bijection between the BD-processes and the FS-processes of a countable net, the latter being defined—in an analogous way—as equivalence classes of firing sequences. Using this, we show that a countable net without binary conflicts has a (unique) largest BD-process.