Summary: In 1995, M. Schellekens [Proc. MFPS 11, Electronic Notes in Theoretical Computer Science 1, 211–232 (1995; Zbl 0910.68135)] introduced the complexity (quasi-metric) space as a part of the development of a topological foundation for the complexity analysis of algorithms. Recently, S. Romaguera and M. Schellekens [Topology Appl. 98, 311–322 (1999; Zbl 0941.54028)] have obtained several quasi-metric properties of the complexity space which are interesting from a computational point of view, via the analysis of the so-called dual complexity space.
Here, we extend the notion of the dual complexity space to the -dual case, with , in order to include some other kinds of exponential time algorithms in this study. We show that the dual -complexity space is isometrically isomorphic to the positive cone of endowed with the asymmetric norm given on by , where . We also obtain some results on completeness and compactness of these spaces.