A Complexity Theory for Hard Enumeration Problems

Nadia Creignou (1) , Markus Kröll (2) , Reinhard Pichler (2) , Sebastian Skritek (2) , Heribert Vollmer (3)

1 LIRICA - Logique, Interaction, Raisonnement et Inférence, Complexité, Algèbre
2 Institute of Information Systems
3 Leibniz Universität Hannover=Leibniz University Hannover

Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enu-meration problems, the tools provided by complexity theory for this important class of problems are very limited. In particular, complexity classes analogous to the polynomial hierarchy and an appropriate notion of problem reduction are missing. In this work, we lay the foundations for a complexity theory of hard enumeration problems by proposing a hierarchy of complexity classes and by investigating notions of reductions for enumeration problems.

Domaines: Complexité [cs.CC]; Intelligence artificielle [cs.AI]; Mathématique discrète [cs.DM]; Logique en informatique [cs.LO]

Nadia Creignou, Markus Kröll, Reinhard Pichler, Sebastian Skritek, Heribert Vollmer. A Complexity Theory for Hard Enumeration Problems. Discrete Applied Mathematics, 2019, 268, pp.191-209. ⟨10.1016/j.dam.2019.02.025⟩. ⟨hal-02439418⟩