Theory of Computing Systems

, Volume 50, Issue 3, pp 446–491 | Cite as

Trichotomies in the Complexity of Minimal Inference

  • Arnaud Durand
  • Miki Hermann
  • Gustav Nordh


We study the complexity of the propositional minimal inference problem. Although the complexity of this problem has been already extensively studied before because of its fundamental importance in nonmonotonic logics and commonsense reasoning, no complete classification of its complexity was found. We classify the complexity of four different and well-studied formalizations of the problem in the version with unbounded queries, proving that the complexity of the minimal inference problem for each of them has a trichotomy (between P, coNP-complete, and Π2P-complete). One of these results finally settles with a positive answer the trichotomy conjecture of Kirousis and Kolaitis (Theory Comput. Syst. 37(6):659–715, 2004). In the process we also strengthen and give a much simplified proof of the main result from Durand and Hermann (Proceedings 20th Symposium on Theoretical Aspects of Computer Science (STACS 2003), pp. 451–462, 2003).


Boolean Function Minimal Model Conjunctive Normal Form Propositional Formula Satisfying Assignment 
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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Equipe de Logique MathématiqueInstitut de Mathématiques de Jussieu (CNRS UMR 7586)Paris cedex 05France
  2. 2.LIX (CNRS UMR 7161)École PolytechniquePalaiseau cedexFrance
  3. 3.Department of Computer and Information SciencesLinköpings UniversitetLinköpingSweden

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