Applications of graph grammar theory to consistency, synchronization and scheduling in data base systems

Abstract

Graph grammar concepts are applied for the design of consistent states and manipulations modeling actions, transactions and schedules for simultaneous executions on data base systems. Especially we show how to use Church-Rosser Theorems for graph grammars to handle synchronization problems for data base systems in a multi-user environment. In this paper theses concepts are applied to a data base system for a library. For reasons of presentation the system is restricted to the basic features of a library but can be extended to more comfortable systems including also generalized data base systems. All manipulation rules are shown to preserve consistency and it is analysed exactly which of theses rules are collateral and for which of them further synchronization mechanisms are necessary. While consistent states are modelled as graphs and manipulation rules (resp. actions) as graph productions transactions correspond to sequences of productions, and schedules to sequences of parallel productions. The application of a schedule to a consistent state yields a “semantical schedule” which transforms the given state to some other state of the system. Sufficient conditions are given for a schedule to be consistent which means that consistent states are transformed into consistent states. Moreover we are able to define a degree of non-parallelism for schedules such that optimal schedules are those with minimal degree with respect to all equivalent ones. Applying results from graph grammar theory we are able to show that for each schedule there is a unique optimal one. A similar result is shown for semantical schedules where the semantical degree of non-parallelism is smaller than the syntactical one in general.