On the Decidability of Non Interference over Unbounded Petri Nets

TL;DR

This paper investigates the decidability of non-interference properties in unbounded Petri nets, providing new results that show certain non-interference properties are decidable despite the undecidability of related equivalence problems.

Contribution

It introduces a novel interpretation of intransitive non-interference for Petri nets and proves the decidability of non-interference properties for a class of infinite state systems.

Findings

Non-interference can be decided over certain unbounded Petri nets.

Language and bisimulation equivalences are undecidable, but non-interference is not.

The paper provides a framework for analyzing security in infinite state systems.

Abstract

Non-interference, in transitive or intransitive form, is defined here over unbounded (Place/Transition) Petri nets. The definitions are adaptations of similar, well-accepted definitions introduced earlier in the framework of labelled transition systems. The interpretation of intransitive non-interference which we propose for Petri nets is as follows. A Petri net represents the composition of a controlled and a controller systems, possibly sharing places and transitions. Low transitions represent local actions of the controlled system, high transitions represent local decisions of the controller, and downgrading transitions represent synchronized actions of both components. Intransitive non-interference means the impossibility for the controlled system to follow any local strategy that would force or dodge synchronized actions depending upon the decisions taken by the controller after the last synchronized action. The fact that both language equivalence and bisimulation equivalence are undecidable for unbounded labelled Petri nets might be seen as an indication that non-interference properties based on these equivalences cannot be decided. We prove the opposite, providing results of decidability of non-interference over a representative class of infinite state systems.