A simple characterization of uniform boundedness for a class of recursions

Detecting bounded recursions is a powerful optimization technique for recursive database query languages, as bounded recursions can be replaced by equivalent nonrecursive definitions. The problem is also of theoretical interest in that varying the class of recursions considered generates problem instances that vary from linearly decidable to NP-hard to undecidable. In this paper we review and clarify the existing definitions of boundedness. We then specify a class of recursions C such that membership in C guarantees that a certain simple condition is necessary and sufficient for boundedness. We use the notion of membership in C to unify and extend previous work on determining decidable classes of bounded recursions.