The Baire Partial Quasi-Metric Space: A Mathematical Tool for Asymptotic Complexity Analysis in Computer Science

@article{CerdUguet2010TheBP,
  title={The Baire Partial Quasi-Metric Space: A Mathematical Tool for Asymptotic Complexity Analysis in Computer Science},
  author={M. A. Cerd{\`a}-Uguet and Michel P. Schellekens and {\'O}scar Valero},
  journal={Theory of Computing Systems},
  year={2010},
  volume={50},
  pages={387-399}
}
In 1994, S.G. Matthews introduced the notion of partial metric space in order to obtain a suitable mathematical tool for program verification (Ann. N.Y. Acad. Sci. 728:183–197, 1994). He gave an application of this new structure to parallel computing by means of a partial metric version of the celebrated Banach fixed point theorem (Theor. Comput. Sci. 151:195–205, 1995). Later on, M.P. Schellekens introduced the theory of complexity (quasi-metric) spaces as a part of the development of a… 
2 Citations

Existence of minima of functions in partial metric spaces and applications to fixed point theory

We first provide new sufficient conditions for the existence of minima of functions defined on 0-complete partial metric spaces. We then apply the obtained results to derive some fixed point results

Fixed point theorems in generalized metric spaces with applications to computer science

It is shown that the Matthews fixed point theorem does not constitute, in principle, an appropriate implement for asymptotic complexity analysis of algorithms, and two fixed point theorems are proved which provide the mathematical basis for a new technique to carry out asymPTotic complexityAnalysis of algorithms via partial metrics.

References

SHOWING 1-10 OF 16 REFERENCES

The Baire Partial Quasi-Metric Space: A Mathematical Tool for Asymptotic Complexity Analysis in Computer Science

It is shown that a slight modification of the well-known Baire partial metric on the set of all words over an alphabet constitutes an appropriate tool to carry out the asymptotic complexity analysis of algorithms via fixed point methods without the need for assuming the convergence condition inherent to the definition of the complexity space in the Schellekens framework.

Bicompleting weightable quasi-metric spaces and partial metric spaces

We show that the bicompletion of a weightable quasi-metric space is a weightable quasi-metric space. From this result we deduce that any partial metric space has an (up to isometry) unique partial

Difference Equations: From Rabbits to Chaos

Preface * Fibonacci Numbers * Homogeneous Linear Recurrence Relations * Finite Difference Equations * Generating Functions * Nonnegative Difference Equations * Leslie's Population Matrix Model *

Nonsymmetric Distances and Their Associated Topologies: About the Origins of Basic Ideas in the Area of Asymmetric Topology

The historic development of what is now often called “Nonsymmetric or Asymmetric Topology” is summarized in Section 2 and in the following, more specific sections the authors discuss thehistoric development of some of the main ideas of the area in greater detail.

Partial Metric Topology

This paper presents a symmetric generalised metric for such topologies, an approach which sheds new light on how metric tools such as Banach's Theorem can be extended to non‐Hausdorff topologies.

An Extensional Treatment of Lazy Data Flow Deadlock

Outline of a Mathematical Theory of Computation

However, Scott does realize that the approach argued for above is simply an argument for an approach that accomodates human understanding of computation and that the operational approach must not be

An Introduction to Lattices and Order

This chapter discusses the structure of finite distributive lattices and finite Boolean algebras, and the role of lattices in algebra in this structure.

Infinite words - automata, semigroups, logic and games