Quantified constraint satisfaction problem on semicomplete digraphs

Abstract

© 2017 ACM. We study the (non-uniform) quantified constraint satisfaction problem QCSP(ℋ)asH ranges over semicomplete digraphs. We obtain a complexity-theoretic trichotomy: QCSP(ℋ) is either in P, is NP-complete, or is Pspace-complete. The largest part of our work is the algebraic classification of precisely which semicomplete digraphs enjoy only essentially unary polymorphisms, which is combinatorially interesting in its own right.