New results on the Baire partial quasi-metric space, fixed point theory and asymptoticcomplexity analysis for recursive programs

Abstract

Abstract In Cerdà-Uguet et al. (Theory Comput. Syst. 50:387-399, 2012), a newmathematical fixed point technique, that uses the so-called Baire partial quasi-metricspace, was introduced with the aim of providing the asymptotic complexity of a class ofrecursive algorithms. The aforementioned technique presents the advantage that requiresless calculations than the quasi-metric original one given by Schellekens (Electron. NotesTheor. Comput. Sci. 1:211-232, 1995). In this paper we continue the study, started inCerdà-Uguet et al. (Theory Comput. Syst. 50:387-399, 2012), on the use ofpartial quasi-metric spaces for asymptotic complexity analysis of algorithms. Concretely,our main purpose is to prove that the Baire partial quasi-metric space is an appropriatemathematical framework for discussing via fixed point arguments the asymptotic complexityof a general class of recursive algorithms to which all the algorithms analyzed inCerdà-Uguet et al. (Theory Comput. Syst. 50:387-399, 2012) belong. Theobtained results are illustrated by means of applying them to yield the complexity of twocelebrated recursive algorithms which don not belong to the class discussed inCerdà-Uguet et al. (Theory Comput. Syst. 50:387-399, 2012). MSC: 47H10, 54E50, 68Q15, 68Q25, 68W40.