Geodesic
A hierarchical decomposition of decision process Petri nets for modeling complex systems
International Journal of Applied Mathematics and Computer Science, Tome 20 (2010) no. 2, pp. 349-366.

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We provide a framework for hierarchical specification called Hierarchical Decision Process Petri Nets (HDPPNs). It is an extension of Decision Process Petri Nets (DPPNs) including a hierarchical decomposition process that generates less complex nets with equivalent behavior. As a result, the complexity of the analysis for a sophisticated system is drastically reduced. In the HDPPN, we represent the mark-dynamic and trajectory-dynamic properties of a DPPN. Within the framework of the mark-dynamic properties, we show that the HDPPN theoretic notions of (local and global) equilibrium and stability are those of the DPPN. As a result in the trajectory-dynamic properties framework, we obtain equivalent characterizations of that of the DPPN for final decision points and stability. We show that the HDPPN mark-dynamic and trajectory-dynamic properties of equilibrium, stability and final decision points coincide under some restrictions. We propose an algorithm for optimum hierarchical trajectory planning. The hierarchical decomposition process is presented under a formal treatment and is illustrated with application examples.
Keywords: hierarchy, decomposition, structuring mechanisms, re-usable components, decision process, DPPN, stability, Lyapunov methods, optimization
Mots-clés : hierarchia, rozkład, składnik wielokrotnego użycia, proces decyzyjny, stabilność, optymalizacja, metoda Lyapunova, DPPN 
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Clempner, J. A hierarchical decomposition of decision process Petri nets for modeling complex systems. International Journal of Applied Mathematics and Computer Science, Tome 20 (2010) no. 2, pp. 349-366. http://geodesic.mathdoc.fr/item/IJAMCS_2010_20_2_a10/

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