Strong Sleptsov Net is Turing-Complete

TL;DR

This paper introduces a strong Sleptsov net, a variant of Petri nets, and proves it is Turing-complete, expanding the understanding of computational power in graphical models of concurrency.

Contribution

It defines and analyzes a strong Sleptsov net, proving its Turing-completeness using a novel simulation of register machines.

Findings

Strong Sleptsov net is Turing-complete.

Firing rules classify nets based on firability.

The proof adapts Peterson's method for inhibitor Petri nets.

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.