Relational algebraic framework for the modelling and analysis of Petri nets

Abstract

Petri nets are a powerful modelling tool for studying reactive, concurrent systems. While various means of analysis for the nets have been developed, a major limitation in the analysis is explosion of global states space in simulation. An efficient method to manage a large states space would overcome such a limitation. This paper proposes a framework for the modelling and analysis of Petri nets using relational database technologies. Within the framework, Petri nets and associated properties are formalized by relations defined in relational algebra. Analysis algorithms are developed based on such formal relations. Thus, our framework not only exploits all advantages of the database system in the management of complex data but also preserves formalism for the modelling and analysis of Petri nets. The framework has been realized in a commercial relational database system using a standard SQL. We demonstrate the feasibility of our methodology by the comparison of the implementation to an implementation in a memory-based environment.