Abstract
In this paper we study the complexity of Hornets, an algebraic extension of object nets. We define a restricted class: safe, elementary Hornets, to guarantee finite state spaces.
We have shown previously that the reachability problem for this class requires at least exponential space, which is a major increase when compared to safe, elementary object nets, which require polynomial space.
Here, we show how a safe, elementary Hornets can be simulated by a safe Eos, which establishes an upper bound for the complexity, since we know that that the reachability problem for safe Eos is PSpace-complete.
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References
Köhler, M., Rölke, H.: Concurrency for mobile object-net systems. Fundamenta Informaticae 54 (2003)
Köhler, M., Rölke, H.: Properties of Object Petri Nets. In: Cortadella, J., Reisig, W. (eds.) ICATPN 2004. LNCS, vol. 3099, pp. 278–297. Springer, Heidelberg (2004)
Köhler-Bußmeier, M., Heitmann, F.: On the expressiveness of communication channels for object nets. Fundamenta Informaticae 93, 205–219 (2009)
Valk, R.: Modelling concurrency by task/flow EN systems. In: 3rd Workshop on Concurrency and Compositionality, St. Augustin, Bonn, Gesellschaft für Mathematik und Datenverarbeitung. GMD-Studien, vol. 191 (1991)
Valk, R.: Object petri nets. In: Desel, J., Reisig, W., Rozenberg, G. (eds.) ACPN 2003, LNCS, vol. 3098, pp. 819–848. Springer, Heidelberg (2004)
Reisig, W.: Petri nets and algebraic specifications. Theoretical Computer Science 80, 1–34 (1991)
Hoffmann, K., Ehrig, H., Mossakowski, T.: High-level nets with nets and rules as tokens. In: Ciardo, G., Darondeau, P. (eds.) ICATPN 2005. LNCS, vol. 3536, pp. 268–288. Springer, Heidelberg (2005)
Lomazova, I.A.: Nested petri nets for adaptive process modeling. In: Avron, A., Dershowitz, N., Rabinovich, A. (eds.) Trakhtenbrot/Festschrift, LNCS, vol. 4800, pp. 460–474. Springer, Heidelberg (2008)
Köhler-Bußmeier, M.: Hornets: Nets within nets combined with net algebra. In: Franceschinis, G., Wolf, K. (eds.) PETRI NETS 2009. LNCS, vol. 5606, pp. 243–262. Springer, Heidelberg (2009)
Köhler-Bußmeier, M., Heitmann, F.: Safeness for object nets. Fundamenta Informaticae 101, 29–43 (2010)
Köhler-Bußmeier, M., Heitmann, F.: Liveness of safe object nets. Fundamenta Informaticae 112, 73–87 (2011)
Köhler-Bußmeier, M.: On the complexity of safe, elementary Hornets. In: Proceedings of the International Workshop on Concurrency, Specification, and Programming (CS&P 2012). CEUR Workshop Proceedings, vol. 928 (2012)
Lipton, R.J.: The reachability problem requires exponential space. Research Report 62, Dept. of Computer science (1976)
Ehrig, H., Mahr, B.: Fundamentals of algebraic Specification. In: EATCS Monographs on TCS. Springer (1985)
Köhler, M.: Reachable markings of object Petri nets. Fundamenta Informaticae 79, 401–413 (2007)
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Köhler-Bußmeier, M., Heitmann, F. (2013). Complexity Results for Elementary Hornets. In: Colom, JM., Desel, J. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2013. Lecture Notes in Computer Science, vol 7927. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38697-8_9
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DOI: https://doi.org/10.1007/978-3-642-38697-8_9
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