Parameterised Counting Classes with Bounded Nondeterminism

04/27/2019

∙

by   Anselm Haak, et al.

∙

0

∙

share

Stockhusen and Tantau (IPEC 2013) introduced the operators paraW and paraBeta for parameterised space complexity classes by allowing bounded nondeterminism with read-only and read-once access, respectively. Using these operators, they could characterise the complexity of many parameterisations of natural problems on graphs. In this article, we study the counting versions of the parameterised space-bounded complexity classes introduced by Stockhusen and Tantau (IPEC 2013). We show that natural path counting problems in digraphs are complete for the newly introduced classes #paraWL and #paraBetaL. Finally, we introduce parameterised counting classes based on branching programs (BPs). We show that parameterised counting classes based on branching programs coincide with the corresponding parameterised space bounded counting classes.