On the Decidability of Non Interference over Unbounded Petri Nets

Eike Best
Philippe Darondeau
Roberto Gorrieri

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.

In Konstantinos Chatzikokolakis and Véronique Cortier: Proceedings 8th International Workshop on Security Issues in Concurrency (SecCo 2010), Paris, France, 30th August 2010, Electronic Proceedings in Theoretical Computer Science 51, pp. 16–33.
Published: 25th February 2011.

ArXived at: http://dx.doi.org/10.4204/EPTCS.51.2 bibtex PDF

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