Abstract
Structure theory is a branch of net theory devoted to investigate the relationship between the structure and the behaviour of net system models. Many of its powerful results have been derived for some subclasses of ordinary net systems. The aim of this contribution is to draw a general perspective of the structure theory for a subclass with Marked Graph-like underlying graph but allowing weights: weighted T-graphs (WTG). Weights are convenient to properly model systems with bulk services and arrivals. Properties of WTG and the corresponding weighted T-systems (WTS) are presented at three different levels: purely structural (e.g. in consistent WTG conservativeness is equivalent to strong connectedness), inter-relationships between the structure and the behaviour (e.g. structural liveness and boundedness is equivalent to consistency and strong connectedness) and liveness and reachability characterizations (e.g. deciding liveness is linear wrt. the 1-norm of the unique minimal T-semiflow of a consistent, even unbounded, WTS). Classical results for Marked Graphs can be derived as corollaries. Nevertheless, even in live and consistent WTS, important properties of Marked Graphs do not hold (e.g. P-semiflows based characterization of reachability).
This work has been partially supported by the projects CICYT TIG-91-0354 of the Spanish Plan Nacional de Investigación, P IT-6/91 of the Aragonese CONAI (DGA), and Esprit BRA 3148 (DEMON).
This work was performed while this author was visiting the University of Zaragoza within Programa Europa of CAI-CONAI (DGA).
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Teruel, E., Chrzastowski-Wachtel, P., Colom, J.M., Silva, M. (1992). On weighted T-systems. In: Jensen, K. (eds) Application and Theory of Petri Nets 1992. ICATPN 1992. Lecture Notes in Computer Science, vol 616. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55676-1_20
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DOI: https://doi.org/10.1007/3-540-55676-1_20
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