{"type":"ScholarlyArticle","title":"A Complete Classification of Complexity in Allens Algebra in the Presence of a Non-Trivial Basic Relation","authors":[{"name":"Andrei A. Krokhin","slug":"andrei-a-krokhin","given":"Andrei A.","family":"Krokhin","affiliation":""},{"name":"Peter Jeavons","slug":"peter-jeavons","given":"Peter","family":"Jeavons","affiliation":""},{"name":"Peter Jonsson","slug":"peter-jonsson","given":"Peter","family":"Jonsson","affiliation":""}],"abstract":"We study fragments of Allen’s algebra that contain a basic relation distinct from the equality relation. We prove that such a fragment is either NPcomplete or else contained in some already known tractable subalgebra. We obtain this result by giving a new uniform description of known maximal tractable subalgebras and then systematically using an algebraic technique for description of maximal subalgebras with a given property. This approach avoids the need for extensive computerassisted search.","doi":null,"url":"https://ijcai.org/proceedings/2001/11","pdf":"https://ijcai.org/proceedings/2001/0011.pdf","markdown":"https://ijcai.org/proceedings/2001/11.md","bibtex":"https://ijcai.org/proceedings/2001/bibtex/11","volume":{"slug":"2001","title":"Proceedings of the Seventeenth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2001","url":"https://ijcai.org/proceedings/2001/","year":2001,"location":"Seattle, Washington, USA","dates":"","editors":"","isbn":"","publisher":"International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":11,"pages":{"first":83,"last":87},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}