QCSP on partially reflexive forests

TL;DR

This paper establishes a complexity dichotomy for the QCSP on partially reflexive forests, classifying problems as either NL or NP-hard, with a refined classification for paths as NL or Pspace-complete.

Contribution

It introduces a new complexity classification for QCSP on partially reflexive forests, including a refined dichotomy for paths, based on connectivity and accessibility conditions.

Findings

QCSP(H) is either in NL or NP-hard for partially reflexive forests.

For partially reflexive paths, QCSP(H) is either in NL or Pspace-complete.

Connectivity and accessibility determine the complexity classification.

Abstract

We study the (non-uniform) quantified constraint satisfaction problem QCSP(H) as H ranges over partially reflexive forests. We obtain a complexity-theoretic dichotomy: QCSP(H) is either in NL or is NP-hard. The separating condition is related firstly to connectivity, and thereafter to accessibility from all vertices of H to connected reflexive subgraphs. In the case of partially reflexive paths, we give a refinement of our dichotomy: QCSP(H) is either in NL or is Pspace-complete.