Qualitative versus quantitative fixed point techniques in computer science

Published in: Quaestiones Mathematicae
Volume 41, issue 1, 2018, pages: 115–127
DOI: 10.2989/16073606.2017.1373712
Author(s): María López-RamírezAir Europa Líneas Aéreas, Spain, Oscar ValeroDepartamento de Ciencias Matemáticas e Informática, Spain


In 1970, a qualitative fixed point technique useful to model the recursive specifications in denotational semantics was developed by means of the celebrated Kleene‘s fixed point theorem. Later on, in 1994 and 1995, quantitative counterparts of the aforesaid technique, but now based on generalized versions of Banach fixed point theorem, were obtained in such a way that the spirit of Kleene‘s technique was preserved. These new techniques are able to provide a measure of the information content degree and this fact has constituted an advantage with respect to the qualitative techniques. The main purpose of this paper is to discern the relationship between the aforementioned qualitative and quantitative fixed point techniques. In particular, we clarify what is the additional real contribution of the quantitative fixed point techniques with respect to the qualitative ones.

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