  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.
