Transitive dependencies in transaction closures

Complex applications consist of a large set of transactions which are interrelated. There are different kinds of dependencies among transactions of a complex application, e.g. termination or execution dependencies which are constraints on the occurrence of significant transaction events. The authors analyze a set of (orthogonal) transaction dependencies. They do not follow traditional approaches which consider advanced transaction structures as a certain kind of nested transactions. They introduce the notion of transaction closure as a generalization of nested transactions. A transaction closure comprises all transactions which are (transitively) initiated by one (root) transaction. By specifying dependencies among transactions of a transaction closure they are then able to define well-known transaction structures like nested transactions as well as advanced activity structures, e.g. workflows, in a common framework. In particular they consider the transitivity property for all kinds of transaction dependencies discussed in the paper. Thus, they are able to conclude how two arbitrary transactions are transitively interrelated. This issue is fundamental for understanding the entire semantics of a complex application