Petri net algebra

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In modern society, computer-based systems have become essential, fundamentally changing how people conduct business. Among the various technologies available, concurrent systems play a crucial role due to the prevalence of concurrent phenomena in applications like control systems, computer networks, digital hardware, business computing, and multimedia systems. These systems exhibit increasing complexity as numerous active components interact. This complexity has been recognized and addressed within the computing science community, leading to the development of several formal models for concurrent systems. This work brings together two widely used formalisms for describing and analyzing these systems: Petri nets and process algebras. Process algebras enable the specification and reasoning about complex concurrent computing system designs using algebraic operators that reflect common programming constructs. In contrast, Petri nets offer a graphical representation of these systems, facilitating efficient verification of correctness and expressing properties related to causality and concurrency in system behavior. This integration of methodologies provides a comprehensive framework for understanding and managing the intricacies of concurrent systems in computing.