Bibliographic Details
| Title: |
Sequence spaces and asymmetric norms in the theory of computational complexity |
| Authors: |
García-Raffi, L.M.1, Romaguera, S., Sánchez-Pérez, E.A.1 |
| Source: |
Mathematical & Computer Modelling. Jul2002, Vol. 36 Issue 1/2, p1. 11p. |
| Subjects: |
Computational complexity, Sequence spaces |
| Abstract: |
In 1995, Schellekens introduced the complexity (quasi-metric) space as a part of the development of a topological foundation for the complexity analysis of algorithms. Recently, Romaguera and Schellekens 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 p-dual case, with p > 1, in order to include some other kinds of exponential time algorithms in this study. We show that the dual p-complexity space is isometrically isomorphic to the positive cone of lp endowed with the asymmetric norm &z.sfnc;.&z.sfnc;+p given on lp by &z.sfnc;x&z.sfnc;+p = [∑n=0∞((xn V0)p)]1/p, where x ≔ (xn)n∊ω. We also obtain some results on completeness and compactness of these spaces. [Copyright &y& Elsevier] |
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| Database: |
Engineering Source |
