Petri nets modeling and analysis using extended bag-theoretic relational algebra

Abstract

Petri nets are a powerful modeling tool for studying reactive, concurrent systems, Analysis of the nets can reveal important information concerning the behavior of a modeled system, While various means for the analysis of the nets has been developed, a major limitation in the analysis, is explosion of large states space in simulation. An efficient method to manage large states space would overcome such a limitation. This paper proposes a framework for the modeling and analysis of Petri nets using relational database technologies. Formalism of the framework is based on a bag-theoretic relational algebra extended from the conventional. Within the framework, Petri nets are formalized by bag relations, and analysis algorithms are developed based on such formal relations. Properties associated with the nets are formalized by queries described in terms of the bag-theoretic relational algebra. The framework has been realized in a commercial relational database system using a standard SQL.