On Compositionality of Boundedness and Liveness for Nested Petri Nets

Authors:
Leonid W. Dworzański;Irina A. Lomazova
Affiliations:
National Research University Higher School of Economics, Moscow, 101000, Russia, leo@mathtech.ru;National Research University Higher School of Economics, Moscow, 101000, Russia and Program Systems Institute of the Russian Academy of Science, Pereslavl-Zalessky, 152020, Russia, i_lomazova@mail ...
Venue:
Fundamenta Informaticae - Concurrency Specification and Programming CS&P
Year:
2012

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Abstract

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.