Algebraic Properties Of Processes for Local Action Systems

Graph rewriting has been used extensively to model the behaviour of concurrent systems and to provide a formal semantics for them. In this paper, we investigate processes for Local Action Systems (LAS); LAS generalize several types of graph rewriting based on node replacement and embedding. An important difference between processes for Local Action Systems and the process notions that have been introduced for other systems, for example, Petri nets, is the presence of a component describing the embedding mechanism. The aim of the paper is to develop a methodology for dealing with this embedding mechanism: we introduce a suitable representation (a dynamic structure) for it, and then investigate the algebraic properties of this representation. This leads to a simple characterization of the configurations of a process and to a number of equational laws for dynamic structures. We illustrate the use of these laws by providing an equational proof of one of the basic results for LAS processes, namely that the construction yielding the result graph of a process behaves well with respect to the sequential composition of processes.