A Small Universal Petri Net

TL;DR

This paper presents a small, universal deterministic inhibitor Petri net with 14 places, capable of simulating a weakly universal Turing machine, demonstrating universality with a compact structure.

Contribution

It introduces a minimal universal Petri net constructed via simulation of a specific weakly universal Turing machine, including a translation from bi-tag systems to Turing machines.

Findings

Constructed a Petri net with 14 places, 29 transitions, and 138 arcs.

Demonstrated universality in the standard sense for Petri nets.

Achieved exponential time complexity in simulation.

Abstract

A universal deterministic inhibitor Petri net with 14 places, 29 transitions and 138 arcs was constructed via simulation of Neary and Woods' weakly universal Turing machine with 2 states and 4 symbols; the total time complexity is exponential in the running time of their weak machine. To simulate the blank words of the weakly universal Turing machine, a couple of dedicated transitions insert their codes when reaching edges of the working zone. To complete a chain of a given Petri net encoding to be executed by the universal Petri net, a translation of a bi-tag system into a Turing machine was constructed. The constructed Petri net is universal in the standard sense; a weaker form of universality for Petri nets was not introduced in this work.