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Showing papers on "Process architecture published in 1977"


Journal ArticleDOI
TL;DR: The problem of deciding whether a Petri net is persistent is reducible to reachability, partially answering a question of Keller, and it is shown that the controllability problem requires exponential space, even for 1-bounded nets.

256 citations


Journal ArticleDOI
TL;DR: This paper discusses Petri nets in the context of the state equation for a linear discrete-time system and shows that the controllability and reachability of a Petri net are related to maximal matchings of its bipartite graph.
Abstract: Petri nets are a versatile modeling device for studying the structure and control of concurrent systems. Petri nets and related graph models have been used for modeling a wide variety of systems from computers to social systems. In order to introduce this interesting modeling device to the researcher in control theory, this paper discusses Petri nets in the context of the state equation for a linear discrete-time system. The controllability concept of dynamic systems is applied to Petri nets for the first time. It is also shown that the controllability and reachability of a Petri net are related to maximal matchings of its bipartite graph.

136 citations


Journal ArticleDOI
TL;DR: After introducing new normal forms for Petri nets, it is proved that the reachability problem is equivalent to the emptiness problem for the intersection of Szilard languages and the methodology presented should also apply to related models for representing parallel processes such as Karp and Miller and Gostelow.
Abstract: We investigate the properties of firing sequences (f.s.) of Petri nets and relate' them to other well-known families of formal languages. We prove in particular that the complement of the f.s. set is context free, and consequently neither the class of f.s. sets (according to some definition) nor Szilard languages are closed with respect to the complement. After introducing new normal forms for Petri nets, we prove that the reachability problem is equivalent to the emptiness problem for the intersection of Szilard languages. 1. INTRODUCTION The focus of this paper is on the formal properties of Petri nets, but the methodology presented should also apply to related models for representing parallel processes such as those by Karp and Miller (1969) and Gostelow

45 citations


01 Aug 1977
TL;DR: A model of concurrent systems having the capability of handling colored representations of control flow has been defined as an extension of an already existing model of parallel systems, the Petri Net Model, whose structure and execution rules have been modified in order to handle the colored tokens.
Abstract: : The problem of representing reentrancy, recursivity and pipe-lining of control in asynchronous structures is examined with the intention of eliminating some of the drawbacks of the other solutions to their problems known so far. A model of concurrent systems having the capability of handling colored representations of control flow has been defined as an extension of an already existing model of parallel systems, the Petri Net Model. The structure and execution rules of Petri Nets have been modified in order to handle the colored tokens. (Author)

13 citations