Strong Sleptsov Net is Turing-Complete (2201.09034v1)

Abstract: It is known that a Sleptsov net, with multiple firing a transition at a step, runs exponentially faster than a Petri net opening prospects for its application as a graphical language of concurrent programming. We provide classification of place-transition nets based on firability rules considering general definitions and their strong and weak variants. We introduce and study a strong Sleptsov net, where a transition with the maximal firing multiplicity fires at a step, and prove that it is Turing-complete. We follow the proof pattern of Peterson applied to prove that an inhibitor Petri net is Turing-complete simulating a Shepherdson and Sturgis register machine. The central construct of our proof is a strong Sleptsov net that checks whether a register value (place marking) equals zero.