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The dynamic optimality conjecture is perhaps the most fundamental open question about binary search trees (BST). It postulates the existence of an asymptotically optimal online BST, i.e. One that is constant factor competitive with any BST on any input access sequence. The two main candidates for dynamic optimality in the literature are splay trees [Sleator and Tarjan, 1985], and Greedy [Lucas, 1988,...
We investigate the size of sets of computable functions using category-theoretic methods (in the sense of the Baire Category theorem). Constructive definitions of no-where dense and meagre set are given and applied to several problems. In particular we apply it to subrecursive degree structures and to a comparison of the power of deterministic and nondeterministic time bounded oracle machines.
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