Alpha: an extension of relational algebra to express a class of recursive queries

An extension of E.F. Codd´s relational algebra (1970) with an alpha (α) operator is presented that allows a large class of natural and useful recursive queries to be expressed, and yet has the property of being efficiently implementable. Formally, this class is a superset of linear recursive queries. Intuitively, this class comprises queries that examine transitive relationships between various instances of an entity. It is believed that this class covers many natural and interesting recursive queries. Examples of such queries include determining parts requirements for manufacturing a product, finding the critical path in a project management network, finding the shortest path between two cities, verifying connectivity between two points of a circuit, etc