Amalgamation of graph transformations with applications to synchronization

Abstract

In the present paper we generalize the well-known PARALLELISM THEOREM for graph derivations to the AMALGAMATION THEOREM. In this theorem the assumption of ‘parallel independence’ is dropped. For each pair of productions together with a relational production (allowing productions to be associated with each other) we construct a single ‘amalgamated’ production. The AMALGAMATION THEOREM states that graph derivations which respect the given associations can be amalgamated to a single derivation via the ‘amalgamated’ production. The amalgamation mechanism can be used to handle synchronization phenomena. The amalgamation concept is applied to synchronization of graph manipulations in a simplified railway control system as well as in GDS, a graph grammar formalism for distributed systems.