Computing complexity distances between algorithms

Salvador Romaguera; Enrique A. Sánchez-Pérez; Oscar Valero

Kybernetika (2003)

  • Volume: 39, Issue: 5, page [569]-582
  • ISSN: 0023-5954

Abstract

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We introduce a new (extended) quasi-metric on the so-called dual p-complexity space, which is suitable to give a quantitative measure of the improvement in complexity obtained when a complexity function is replaced by a more efficient complexity function on all inputs, and show that this distance function has the advantage of possessing rich topological and quasi-metric properties. In particular, its induced topology is Hausdorff and completely regular. Our approach is applied to the measurement of distances between infinite words over the decimal alphabet and some advantages of our computations with respect to the ones that provide the classical Baire metric are discussed. Finally, we show that the application of fixed point methods to the complexity analysis of Divide and Conquer algorithms, presented by M. Schellekens (Electronic Notes in Theoret. Comput. Sci.1(1995)), can be also given from our approach.

How to cite

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Romaguera, Salvador, Sánchez-Pérez, Enrique A., and Valero, Oscar. "Computing complexity distances between algorithms." Kybernetika 39.5 (2003): [569]-582. <http://eudml.org/doc/33666>.

@article{Romaguera2003,
abstract = {We introduce a new (extended) quasi-metric on the so-called dual p-complexity space, which is suitable to give a quantitative measure of the improvement in complexity obtained when a complexity function is replaced by a more efficient complexity function on all inputs, and show that this distance function has the advantage of possessing rich topological and quasi-metric properties. In particular, its induced topology is Hausdorff and completely regular. Our approach is applied to the measurement of distances between infinite words over the decimal alphabet and some advantages of our computations with respect to the ones that provide the classical Baire metric are discussed. Finally, we show that the application of fixed point methods to the complexity analysis of Divide and Conquer algorithms, presented by M. Schellekens (Electronic Notes in Theoret. Comput. Sci.1(1995)), can be also given from our approach.},
author = {Romaguera, Salvador, Sánchez-Pérez, Enrique A., Valero, Oscar},
journal = {Kybernetika},
keywords = {invariant extended quasi-metric; complexity function; balanced quasi-metric; infinite word; Baire metric; contraction mapping; Divide & Conquer algorithm; invariant extended quasi-metric; complexity function; balanced quasi-metric; infinite word; Baire metric},
language = {eng},
number = {5},
pages = {[569]-582},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Computing complexity distances between algorithms},
url = {http://eudml.org/doc/33666},
volume = {39},
year = {2003},
}

TY - JOUR
AU - Romaguera, Salvador
AU - Sánchez-Pérez, Enrique A.
AU - Valero, Oscar
TI - Computing complexity distances between algorithms
JO - Kybernetika
PY - 2003
PB - Institute of Information Theory and Automation AS CR
VL - 39
IS - 5
SP - [569]
EP - 582
AB - We introduce a new (extended) quasi-metric on the so-called dual p-complexity space, which is suitable to give a quantitative measure of the improvement in complexity obtained when a complexity function is replaced by a more efficient complexity function on all inputs, and show that this distance function has the advantage of possessing rich topological and quasi-metric properties. In particular, its induced topology is Hausdorff and completely regular. Our approach is applied to the measurement of distances between infinite words over the decimal alphabet and some advantages of our computations with respect to the ones that provide the classical Baire metric are discussed. Finally, we show that the application of fixed point methods to the complexity analysis of Divide and Conquer algorithms, presented by M. Schellekens (Electronic Notes in Theoret. Comput. Sci.1(1995)), can be also given from our approach.
LA - eng
KW - invariant extended quasi-metric; complexity function; balanced quasi-metric; infinite word; Baire metric; contraction mapping; Divide & Conquer algorithm; invariant extended quasi-metric; complexity function; balanced quasi-metric; infinite word; Baire metric
UR - http://eudml.org/doc/33666
ER -

References

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