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On Compositionality of Boundedness and Liveness for Nested Petri Nets

Dworzański L. W., Lomazova I.A.

Fundamenta Informaticae

2012

Vol. 120, nr 3/4

275-293

Nested Petri nets (NP-nets) are Petri nets with net tokens. The liveness and boundedness problems are undecidable for two-level NP-nets [14]. Boundedness is in EXPSPACE and liveness is in EXPSPACE or worse for plain Petri nets [6]. However, for some restricted classes, e.g. for plain free-choice Petri nets, problems become more amenable to analysis. There is a polynomial time algorithm to check if a free-choice Petri net is live and bounded [4]. In this paper we prove, that for NP-nets boundedness can be checked in a compositional way, and define restrictions, under which liveness is also compositional. These results give a base to establish boundedness and liveness for NP-nets by checking these properties for separate plain components, which can belong to tractable Petri net subclasses, or be small enough for model checking.

Petri nets and resource bisimulation

Bashkin V.A., Lomazova I.A.

Fundamenta Informaticae

2003

Vol. 55, nr 2

101-114

Resources are defined as submultisets of Petri net markings. Two resources are called similar if replacing one of them by another in any marking doesn't change the Petri net's behavior. We define the relations of resource similarity and resource bisimulation and show that they are finitely based. In this paper the resource bisimulation is studied for different classes of Petri nets: ordinary Petri nets, high-level Petri nets and nested Petri nets - Petri nets with Petri nets as tokens.

Modeling Dynamic Objects in Distributed Systems with Nested Petri Nets

Lomazova I.A.

Fundamenta Informaticae

2002

Vol. 51, nr 1,2

121-133

Nested Petri nets (NP-nets) is a Petri net extension, allowing tokens in a net marking to be represented by marked nets themselves. The paper discusses applicability of NP-nets for modeling task planning systems, multi-agent systems and recursive-parallel systems. A comparison of NP-nets with some other formalisms, such as OPNs of R. Valk, recursive parallel programs of O. Kushnarenko and Ph. Schnoebelen and process algebras is given. Some aspects of decidability for object-oriented Petri net extensions are also discussed.

Nested Petri Nets: Multi-level and Recursive Systems

Lomazova I.A.

Fundamenta Informaticae

2001

Vol. 47, nr 3,4

283-293

Nested Petri nets (NP-nets) is a formalism for modeling hierarchical multi-agent systems. Tokens in nested Petri nets are elements represented by nets themselves. The paper continues investigating semantic properties of NP-nets, started in [10], where two-level NP-nets were studied. Here we consider multi-level and recursive NP-nets, for which decidability of termination and some other properties are proved. A comparison of NP-nets with other Petri net models is given.

Nested Petri nets - a formalism for specification and verification of multi-agent distributed systems

Lomazova I.A.

Fundamenta Informaticae

2000

Vol. 43, Nr 1-4

195-214

Nested Petri nets is a formalism for modeling hierarchical multi-agent systems. Tokens in nested Petri nets are elements represented by nets themselves. Decidability of some crucial for verification problems shows that, in spite of their "unflat" structure, nested Petri nets maintain significant properties of ordinary Petri nets. A comparison with some other Petri net models is given. The formalism allows generalization to a recursive case, when a nested Petri net may generate its own copy as its element. Two simple examples illustrate the approach.