Computational issues in exploiting dependent and-parallelism in logic programming: Leftness detection in dynamic search trees

We present efficient Pure Pointer Machine (PPM) algorithms to test for "leftness" in dynamic search trees and related problems. In particular, we show that the problem of testing if a node x is in the leftmost branch of the subtree rooted in node y, in a dynamic tree that grows and shrinks at the leaves, can be solved on PPMs in worst-case O((lg lg n)(2)) time per operation in the semi-dynamic case-i.e., all the operations that add leaves to the tree are performed before any other operations-where n is the number of operations that affect the structure of the tree. We also show that the problem can be solved on PPMs in amortized O((lg lg n)(2)) time per operation in the fully dynamic case.