A Study on the Structure of Linear Recursion

We study a general class of single linear recursions and the properties of their expansions by analyzing the structures of the recursions. We show that the expansions of a linear recursion of this class are very regular in that the variable connections are heavily shared and change periodically with respect to the expansions. The variable connections can be precisely characterized as static bindings and chain connections. We conclude that a single linear recursion under our assumptions either is bounded or can be expressed as chain recursions. This study contributes to query processing, because it provides the basis for rule compilation as a general and powerful technique for query processing. Combined with query information, the expansion properties of the recursion provide optimized query-processing plans.