Petri net with reset arc

Question

How to find an ordinary Petri net equivalent to Petri net with reset arc? This ordinary net have to respect the semantic of reset Petri net.

Best regards.

Answer 1

It is not possible to find an ordinary Petri Net that would be equivalent to an arbitrary Petri net with reset arcs in any meaningful sense.

It is known that the class of Petri nets with at least one reset arc is strictly more expressible than ordinary Petri Nets.

In their 1977 paper Toshiro Araki and Tadao Kasami proved by reduction of Minsky counter automata (see Theorem 5) to Petri nets with reset arcs that the reachability problem for Petri nets with reset arcs is undecidable.

While in 1981 Ernst Mayr presented an algorithm for the reachability problem for ordinary Petri nets.

If a reduction from Petri nets with reset arcs to ordinary Petri nets could be algorithmically defined the reachability problem for both classes would have the same decidability status. The two results show that this is not the case, therefore such reduction is not possible.

The papers cited above require a bit of technical knowledge to read that is not generally expected from CompSci students. For a background on the subject I would suggest the original "Computation: Finite and Infinite Machines" by M.L. Minsky or any modern introductory text on Logic in Computer Science.