Concurrent graph and term graph rewriting

Abstract

Graph Rewriting Systems are a powerful formalism for the specification of parallel and distributed systems, and the corresponding theory is rich of results concerning parallelism and concurrency. I will review the main results of the theory of concurrency for the algebraic approach to graph rewriting, emphasizing the relationship with the theory of Petri nets. In fact, graph rewriting systems can be regarded as a proper generalization of Petri nets, where the current state of a system is described by a graph instead of by a collection of tokens. Recently, this point of view allowed for the generalization to graph rewriting of some interesting results and constructions of the concurrent semantics of nets, including processes, unfoldings, and categorical semantics based on pair of adjoint functors.