Dynamic Constraints and Object Migration

A “role set” is the set of classes in a class hierarchy where an object may reside simultaneously. A “migration pattern” is a sequence of role sets that an object can migrate through. We define a “migration inventory”, which is a set of migration patterns, as a dynamic integrity constraint on object migration. We consider three update languages: SL which has five operators, CSL+ which extends SL with positive conditionals, and CSL which allows both positive and negative conditionals. Three subclasses of migration patterns of transactions are studied which are immediate-start, proper, and lazy patterns. It is shown that the family of all (immediate-start, proper, or lazy) migration patterns of every set of SL transactions is a regular set and the converse also holds. In particular, testing “satisfiability” of an inventory by a set of transactions is decidable. For the extended languages, we give a weaker characterization. The family of all (immediate-start, proper, or lazy) migration patterns of every set of CSL (CSL+) transactions is recursively enumerable (r.e.). However, every r.e. inventory can be the family of all migration patterns of some set of CSL+ (CSL) transactions and be a left quotient of the family of immediate-start migration patterns of another set of CSL+ (CSL) transactions by a regular set. Although the exact characterizations of immediate-start, proper, lazy migration patterns of CSL+ (CSL) transactions are still open, it is proved that every context-free inventory can be the family of proper and immediate-start migration patterns of some CSL+ (CSL) transactions. Testing satisfiability of an inventory by a set of CSL (CSL+) transactions is unfortunately undecidable.