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Hierarchical Reachability Graph Generation for Petri Nets

Hierarchical Reachability Graph Generation for Petri Nets

Hierarchical Reachability Graph Generation for Petri

Formal Methods in System Design, 21, 281–315, 2002c○ 2002 Kluwer Academic Publishers. Manufactured in The Netherlands.Hierarchical Reachability Graph Generationfor Petri NetsPETER BUCHHOLZFakultät Informatik, TU Dresden, D-01062 Dresden, Germanyp.buchholz@inf.tu-dresden.dePETER KEMPERInformatik IV, Universität Dortmund, D-44221 Dortmund, Germanykemper@ls4.cs.uni-dortmund.deReceived November 18, 1997; Accepted December 3, 2001Abstract. Reachability analysis is the most general approach to the analysis of Petri nets. Due to the wellknownproblem of state-space explosion, generation of the reachability set and reachability graph with the knownapproaches often becomes intractable even for moderately sized nets. This paper presents a new method to generateand represent the reachability set and reachability graph of large Petri nets in a compositional and hierarchical way.The representation is related to previously known Kronecker-based representations, and contains the completeinformation about reachable markings and possible transitions. Consequently, all properties that it is possible forthe reachability graph to decide can be decided using the Kronecker representation. The central idea of the newtechnique is a divide and conquer approach. Based on net-level results, nets are decomposed, and reachabilitygraphs for parts are generated and combined. The whole approach can be realized in a completely automated wayand has been integrated in a Petri net-based analysis tool.Keywords:Petri nets, reachability set, reachability graph, hierarchical structure, invariant analysis1. IntroductionPetri nets (PNs) are an established formalism for describing and analyzing dynamic systems.Among the large number of available analysis techniques, the generation of the set ofall reachable markings and all possible transitions is the most general approach that istheoretically applicable for every bounded net. The resulting graph is called the reachabilitygraph (RG) or occurrence graph. The set of reachable markings is called the reachability set(RS). Reachable markings of the PN build the vertices of the graph, and transitions describethe edges. Edges may be labeled with the corresponding transition identifiers from the PNdescription. The RG contains the full information about the dynamic behavior of the PNand can be easily analyzed to gain results about the functional behavior as required for theverification of system properties. RGs are generated by an algorithm computing all successormarkings for discovered markings, starting with the initial marking of the net. This approachis conceptually simple and is integrated in most software tools developed for the analysisof PNs. In practice, unfortunately, the size of RGs often grows exponentially with the sizeof the PN in terms of places and tokens. Hence, RG generation is usable only for relativelysmall nets, much smaller than most practically relevant examples are. Consequently, many

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