Efficient Restrictions of Immediate Observation Petri Nets

TL;DR

This paper investigates restrictions of immediate observation Petri nets to reduce the complexity of the reachability problem, making it more feasible for applications in distributed protocols and chemical networks.

Contribution

It introduces two restrictions on IO nets that lower the reachability problem complexity from PSPACE-complete to NP-complete and polynomial time.

Findings

NP-complete reachability for the first restriction

Polynomial-time reachability for the second restriction

Applications in distributed protocols and chemical reaction networks

Abstract

In a previous paper we introduced immediate observation Petri nets, a subclass of Petri nets with application domains in distributed protocols (population protocols) and theoretical chemistry (chemical reaction networks). IO nets enjoy many useful properties, but like the general case of conservative Petri nets they have a PSPACE-complete reachability problem. In this paper we explore two restrictions of the reachability problem for IO nets which lower the complexity of the problem drastically. The complexity is NP-complete for the first restriction with applications in distributed protocols, and it is polynomial for the second restriction with applications in chemical settings.