Abstract processes and conflicts in place/transition systems

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

“…We refer to [BD87,GGS21] for an explanation of this definition and further examples. Here we only give the processes of Fig.…”

“…In [BD87, Definition 7.8] swapping equivalence-denoted ≡ ∞ 1 -is defined in terms of reachable B-cuts. In [GGS21] this definition was reformulated as follows, also introducing the associated preorder ⊑ ∞ 1 .…”

“…GR-processes can be seen as an unsatisfactory formalisation of the intuitive concept of a run, since there exist conflict-free 1 systems with multiple maximal GR-processes. We refer to [GGS11a,GGS21] and the many references therein for an example and further discussion. On the other hand, BD-processes can be seen as unsatisfactory, because there exist systems which do have conflicts, yet still have a unique maximal BD-process.…”

“…In [GGS11a,GGS21] we propose a subclass of P/T systems, called structural conflict nets, more general then the well-known class of safe nets. On these nets BD-processes are a good formalisation of runs, for we showed that a structural conflict net has a largest BD-process if and only if the net is conflict-free.…”

“…In this paper we will show that the "if" part of the above-mentioned correspondence also holds for general countable P/T systems: a countable conflict-free P/Tsystem has a largest BD-process. 2 However, it turns out that the proof of this result is much more complicated than the special case for structural conflict nets established in [GGS21]. 3 Best and Devillers [BD87] defined a swapping transformation also on the firing sequences of a net, allowing two adjacent transitions to be swapped if they can be fired concurrently.…”