Aggregation of asymmetric distances in Computer Science

In this paper we provide a general description of how to combine a collection (not necessarily finite) of asymmetric distances in order to obtain a single one as output. To this end we introduce the notion of asymmetric distance aggregation function that generalizes the well-known one for distance spaces given by Borsik and Doboš [J. Borsik, J. Doboš, On a product of metricspaces, Math. Slovaca 31 (1981) 193–205]. Among other results, a characterization of such functions is obtained in terms of monotony and subadditivity. Finally, we relate our results to Computer Science. In particular we show that the mathematical formalism based on complexity distances, which has been introduced by Romaguera and Schellekens [S. Romaguera, M. Schellekens, Quasi-metric properties of complexity spaces, Topol. Appl. 98 (1999) 311–322] for the complexity analysis of programs and algorithms, can be obtained as a particular case of our new framework using appropriate asymmetric aggregation distance functions.