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A decidable class of bounded recursions

Detecting bounded recursions is a powerful optimization technique for recursions database query languages as bounded recursions can be replaced by equivalent nonrecursive definitions. The problem is of theoretical interest because by varying the class of recursions considered one can generate 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 sample criterion that guarantees that the condition in Vaughton [7] is necessary and sufficient for boundedness. The programs satisfying this criterion subsume and extend previously known decidable classes of bounded linear recursions.