Trichotomies in the Complexity of Minimal Inference
2012 (English)In: Theory of Computing Systems, ISSN 1432-4350, E-ISSN 1433-0490, Vol. 50, no 3, 446-491 p.Article in journal (Refereed) Published
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 I P-2-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).
Place, publisher, year, edition, pages
Springer Verlag (Germany) , 2012. Vol. 50, no 3, 446-491 p.
Engineering and Technology
IdentifiersURN: urn:nbn:se:liu:diva-75268DOI: 10.1007/s00224-011-9320-0ISI: 000299515500004OAI: oai:DiVA.org:liu-75268DiVA: diva2:505955
Funding Agencies|Swedish Research Council (VR)|2008-4675|Swedish-French Foundation|||ANR-07-BLAN-0327|2012-02-272012-02-242012-08-16