Abstract
Transient secure association has been widely accepted as a possible alternative to traditional authentication in the context of Ubiquitous Computing. Two components in a distributed system with transient secure association may share a master-slave relationship, which creates a hierarchical but dynamic structure of components. In this paper we develop several formal models for distributed systems with transient secure association, with incremental expressive power, all based on Petri nets. The first model, that we call transient secure association (TSA) systems, considers finitely many components. Then we consider a small extension of TSA systems, in which slaves are initialized whenever a master-slave relation is broken. Last, we define unbounded TSA (uTSA) systems, for which the number of components is not bounded. For each of the defined formalisms, we establish a link to a known class of Petri nets, thus inheriting the corresponding (un)decidability results from them.
Similar content being viewed by others
Notes
Other standard approaches rely on infinite sets of initial states.
Not to be confused with any equivalence or preorder in Van Glabbeek’s spectrum [13].
We call it weak isomorphism even if, as defined, it is not a symmetric relation.
Multiset subtraction is only used in that case in the paper.
We define it in this way to follow our generic definition of Petri nets, though it is clearly equivalent to the definition using total functions to \(\mathbb {N}\).
Actually, home space is only decidable for linear sets of final markings, as is the case of the set of final markings of our example.
Without that assumption, we just need to define \(init(N_i)\) accordingly.
Other “creating” policies can be envisaged, as creating components that are initially imprinted by the creating one.
Actually, we could add some control states that sequentialize the simulating net so that, in particular, no other transition can be fired during the simulation of a killing. We have preferred not to do so for simplicity of our construction.
This class was called asynchronous \(\nu \)-PN in [18].
References
Abdulla, P.A., Chen, Y., Delzanno, G., Haziza, F., Hong, C., Rezine, A.: Constrained monotonic abstraction: a CEGAR for parameterized verification. In: Proceedings of 21st International Conference on Concurrency Theory, CONCUR’10, vol. 6296 of LNCS, pp. 86–101. Springer (2010)
Abdulla, P.A., Delzanno, G., Van Begin, L.: A classification of the expressive power of well-structured transition systems. Inf. Comput. 209(3), 248–279 (2011)
Bruni, R., Montanari, U.: Executing transactions in zero-safe nets. In: Proceedings of 21st International Conference on Application and Theory of Petri Nets, ICATPN’00, vol. 1825 of LNCS, pp. 83–102. Springer (2000)
Carbone, M., Nielsen, M., Sassone, V.: A calculus for trust management. In: Proceedings of 24th International Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS’04, vol. 3328 of LNCS, pp. 161–173. Springer (2004)
Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking, MIT Press, Cambridge, MA (1999)
Desel, J., Reisig, W. (eds.): Place/transition Petri nets. In: Lectures on Petri Nets I: Basic Models, vol. 1491 of LNCS, pp. 122–173. Springer (1998)
Dufourd, C., Finkel, A., Schnoebelen, Ph.: Reset nets between decidability and undecidability. In: Proceedings of 25th International Colloquium on Automata, Languages and Programming, ICALP’98, vol. 1443 of LNCS, pp. 103–115. Springer (1998)
Esparza, J., Nielsen, M.: Decidability issues for Petri nets—a survey. Bull. EATCS 52, 244–262 (1994)
de Frutos-Escrig, D., Johnen, C.: Decidability of home space property. Report LRI-503, Laboratoire de Recherche en Informatique, Univ. de Paris-Sud, Centre d’Orsay (1989)
Ganty, P., Raskin, J.-F., van Begin, L.: A complete abstract interpretation framework for coverability properties of WSTS. In: Proceedings of 7th Internarional Conference on Verification, Model Checking, and Abstract Interpretation, VMCAI’06, vol. 3855 of LNCS, pp. 49–64. Springer (2006)
Geeraerts, G., Raskin, J.-F., van Begin, L.: Expand, enlarge and check: new algorithms for the coverability problem of WSTS. J. Comput. Syst. Sci. 72(1), 180–203 (2006)
Geeraerts, G., Heußner, A., Praveen, M., Raskin, J.-F.: \(\omega \)-Petri nets. In: Proceedings of 34th International Conference on Application and Theory of Petri Nets and Concurrency, PETRI NETS’13, vol. 7927 of LNCS, pp. 49–69. Springer (2013)
van Glabbeek, R.J.: The linear time-branching time spectrum (extended abstract). In: Theories of Concurrency: Unification and Extension, CONCUR’90, vol. 458 of LNCS, pp. 278–297. Springer (1990)
Haddad, S., Poitrenaud, D.: Recursive Petri nets. Acta Informatica 44(7–8), 463–508 (2007)
Jančar, P.: Decidability of a temporal logic problem for Petri nets. Theor. Comput. Sci. 74, 71–93 (1990)
Kruskal, J.B.: Well-quasi-ordering, the tree theorem, and Vazsonyi’s conjecture. Trans. Am. Math. Soc. 95(2), 210–225 (1960)
Lomazova, I.: Nested Petri nets: multi-level and recursive systems. Fundamenta Informaticae 47, 283–293 (2001)
Martos-Salgado, M., Rosa-Velardo, F.: Dynamic soundness in resource-constrained workflow nets. In: Proceedings of Formal Techniques for Distributed Systems, Joint 13th IFIP WG 6.1 International Conference, FMOODS’11, and 30th IFIP WG 6.1 International Conference, FORTE’11, vol. 6722 of LNCS, pp. 259–273. Springer (2011)
Meyer, R.: On boundedness in depth in the \(\pi \)-calculus. In: Proceedings of 5th IFIP International Conference on Theoretical Computer Science, TCS’08, IFIP 20th World Computer Congress, TC 1, Foundations of Computer Science, pp. 477–489. Springer (2008)
Milner, R.: Theories for the global ubiquitous computer. In: Proceedings of 7th International Conference on Foundations of Software Science and Computation Structures, FoSSaCS’04, vol. 2987 of LNCS, pp. 5–11. Springer (2004)
Minsky, M.L.: Computation: Finite and Infinite Machines. Prentice-Hall Inc., Englewood Cliffs, NJ (1967)
Richard, G.G.: Service advertisement and discovery: enabling universal device cooperation. IEEE Internet Comput. Arch. 4(5), 18–26 (2000)
Rosa-Velardo, F.: Petri nets for the verification of ubiquitous systems with transient secure association. In: Proceedings of 4th International Conference on Ubiquitous Intelligence and Computing, UIC’07, vol. 4611 of LNCS, pp. 1148–1158. Springer (2007)
Rosa-Velardo, F., de Frutos-Escrig, D.: Decidability problems in Petri nets with names and replication. Fundamenta Informaticae 105(3), 291–317 (2010)
Rosa-Velardo, F., de Frutos-Escrig, D.: Decidability and complexity of Petri nets with unordered data. Theor. Comput. Sci. 412(34), 4439–4451 (2011)
Rosa-Velardo, F., Martos-Salgado, M.: Multiset rewriting for the verification of depth bounded processes with name binding. Inf. Comput. 215, 68–87 (2012)
Schnoebelen, P.: Revisiting Ackermann-hardness for lossy counter machines and reset Petri nets. In: Proceedings of 35th International Symposium on Mathematical Foundations of Computer Science, MCFS’10, vol. 6281 of LNCS, pp. 616–628. Springer (2010)
Siddiqui, M.S., Hong, C.S.: Security issues in wireless mesh networks. In: Proceedings of International Conference on Multimedia and Ubiquitous Engineering. IEEE Computer Society, pp. 717–722 (2007)
Stajano, F., Anderson, R.J.: The resurrecting duckling: security issues for ad-hoc wireless networks. In: Proceedings of 7th International Workshop on Security Protocols, vol. 1796 of LNCS, pp. 172–194. Springer (1999)
Stajano, F.: Security for Ubiquitous Computing. Wiley Series in Communications Networking & Distributed Systems. Wiley, London (2002)
Valk, R.: Object Petri nets. In: Proceedings of 24th International Conference on Applications and Theory of Petri Nets, ICATPN’03, vol. 3098 of LNCS, pp. 819–848. Springer (2004)
van der Aalst, W.M.P., van Hee, K.M.: Workflow Management: Models, Methods, and Systems. MIT Press, Cambridge, MA (2002)
Want, R.: Enabling ubiquitous sensing with RFID. Computer 37(4), 84–86 (2004)
Weiser, M.: Some computer science issues in ubiquitous computing. Commun. ACM 36(7), 74–84 (1993)
Weiser, M.: The Computer for the 21st Century. Human–Computer Interaction: Toward the Year 2000, pp. 933–940. Morgan Kaufmann Publishers Inc., Los Altos, CA (1995)
Acknowledgments
The author would like to thank the anonymous referees for their valuable comments, that have increased the quality of this paper. This work is partially supported by the Spanish projects DESAFIOS10 TIN2009-14599-C03-01, STRONGSOFT TIN2012-39391-C04-04 and the Comunidad de Madrid program PROMETIDOS S2009/TIC-1465.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rosa-Velardo, F. Petri nets with name creation for transient secure association. Acta Informatica 50, 403–436 (2013). https://doi.org/10.1007/s00236-013-0188-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00236-013-0188-0