AUTHOR=Ferrarotti Flavio , González Senén , Schewe Klaus-Dieter , Turull-Torres José María 

TITLE=Uniform Polylogarithmic Space Completeness

JOURNAL=Frontiers in Computer Science

VOLUME=4

YEAR=2022

URL=https://www.frontiersin.org/journals/computer-science/articles/10.3389/fcomp.2022.845990

DOI=10.3389/fcomp.2022.845990

ISSN=2624-9898

ABSTRACT=<p>It is well-known that polylogarithmic space (PolyL for short) does not have complete problems under logarithmic space many-one reductions. Thus, we propose an alternative notion of completeness inspired by the concept of uniformity studied in circuit complexity theory. We then prove the existence of a uniformly complete problem for PolyL under this new notion. Moreover, we provide evidence that uniformly complete problems can help us to understand the still unclear relationship between complexity classes such as PolyL and polynomial time.</p>