The Banach Contraction Principle in Fuzzy Quasi-metric Spaces and in Product Complexity Spaces: Two Approaches to Study the Cost of Algorithms with a Finite System of Recurrence Equations

摘要

Considering recursiveness as a unifying theory for algorithm related problems, we take advantage of algorithms formulation in terms of recurrence equations to show the existence and uniqueness of solution for the recurrence equations associated to a kind of algorithms defined as a finite system of procedures by applying the Banach contraction principle both in a suitable product of fuzzy quasi-metrics defined on the domain of words and in the product quasi-metric space of complexity spaces.