Sleptsov Nets are Turing-complete

TL;DR

This paper proves that Sleptsov nets are Turing-complete, significantly advancing previous results by providing a concise construction and clarifying the firing rules that distinguish SNs from Petri nets.

Contribution

It establishes the Turing-completeness of Sleptsov nets with a simple, direct proof, improving upon prior work that required stronger restrictions.

Findings

Sleptsov nets are Turing-complete.

SNs fire enabled transitions at maximal multiplicity in a single step.

The proof simplifies understanding of SN computational power.

Abstract

The present paper proves that a Sleptsov net (SN) is Turing-complete, that considerably improves, with a brief construct, the previous result that a strong SN is Turing-complete. Remind that, unlike Petri nets, an SN always fires enabled transitions at their maximal firing multiplicity, as a single step, leaving for a nondeterministic choice of which fireable transitions to fire. A strong SN restricts nondeterministic choice to firing only the transitions having the highest firing multiplicity.