Denotational semantics for programming languages, balanced quasi-metrics and fixed points

Authors:
J. Rodríguez-López;S. Romaguera;O. Valero
Affiliations:
Departamento de Matemática Aplicada, Universidad Politécnica de Valencia - IMPA-UPV, Valencia, Spain;Departamento de Matemática Aplicada, Universidad Politécnica de Valencia - IMPA-UPV, Valencia, Spain;Departamento de Matemáticas e Informática, Universidad de las Islas Baleares, Baleares, Spain
Venue:
International Journal of Computer Mathematics - Recent Advances in Computational and Applied Mathematics in Science and Engineering
Year:
2008

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Abstract

A new mathematical model is introduced for the study of the domain of words. We do it by means of the introduction of a suitable balanced quasi-metric on the set of all words over an alphabet. It will be shown that this construction has better quasi-metric and topological properties than several classical constructions. We also prove a fixed point theorem which allows us to develop an application for the study of probabilistic divide and conquer algorithms.