Abstract
We study the (non-uniform) quantified constraint satisfaction problem QCSP\((\mathcal{H})\) as \(\mathcal{H}\) ranges over partially reflexive forests. We obtain a complexity-theoretic dichotomy: QCSP\((\mathcal{H})\) is either in NL or is NP-hard. The separating condition is related firstly to connectivity, and thereafter to accessibility from all vertices of \(\mathcal{H}\) to connected reflexive subgraphs. In the case of partially reflexive paths, we give a refinement of our dichotomy: QCSP\((\mathcal{H})\) is either in NL or is Pspace-complete.
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Martin, B. (2011). QCSP on Partially Reflexive Forests. In: Lee, J. (eds) Principles and Practice of Constraint Programming – CP 2011. CP 2011. Lecture Notes in Computer Science, vol 6876. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23786-7_42
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DOI: https://doi.org/10.1007/978-3-642-23786-7_42
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