<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></abstract>

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.

A hierarchical decomposition of decision process Petri nets for modeling complex systems

Center for Computing Research, National Polytechnic Institute (CIC-IPN), Av. Juan de Dios Batiz s/n, Edificio CIC, Col. Nueva Industrial Vallejo 07738 Mexico City

International Journal of Applied Mathematics and Computer Science

We provide a framework for hierarchical specification called Hierarchical Decision Process Petri Nets (HDPPNs). It is an extension of Decision Process Petri...

A hierarchical decomposition of decision process Petri nets for modeling complex systems

Published Online: Jul 02, 2010

Page range: 349 - 366

DOI: https://doi.org/10.2478/v10006-010-0026-2

Keywords
hierarchy, decomposition, structuring mechanisms, re-usable components, decision process, DPPN, stability, Lyapunov methods, optimization

This content is open access.

A hierarchical decomposition of decision process Petri nets for modeling complex systems

Published Online: Jul 02, 2010

Page range: 349 - 366

DOI: https://doi.org/10.2478/v10006-010-0026-2

Keywordshierarchy, decomposition, structuring mechanisms, re-usable components, decision process, DPPN, stability, Lyapunov methods, optimization

This content is open access.

Keywords
hierarchy, decomposition, structuring mechanisms, re-usable components, decision process, DPPN, stability, Lyapunov methods, optimization