{"type":"ScholarlyArticle","title":"New Canonical Representations by Augmenting OBDDs with Conjunctive Decomposition (Extended Abstract)","authors":[{"name":"Yong Lai","slug":"yong-lai","given":"Yong","family":"Lai","affiliation":"College of Computer Science and Technology Jilin University , China"},{"name":"Dayou Liu","slug":"dayou-liu","given":"Dayou","family":"Liu","affiliation":"College of Computer Science and Technology Jilin University , China"},{"name":"Minghao Yin","slug":"minghao-yin","given":"Minghao","family":"Yin","affiliation":"Department of Computer Science Northeast Normal University , China"}],"abstract":"We identify two families of canonical representations called ROBDD[/\\i^]_C and ROBDD[/\\T^,i]_T by augmenting ROBDD with two types of conjunctive decompositions. These representations cover the three existing languages ROBDD, ROBDD with as many implied literals as possible (ROBDD-L_&infin), and AND/OR BDD. We introduce a new time efficiency criterion called rapidity which reflects the idea that exponential operations may be preferable if the language can be exponentially more succinct. Then we demonstrate that the expressivity, succinctness and operation rapidity do not decrease from ROBDD[/\\T^,i]_T to ROBDD[/\\i^]_C, and then to ROBDD[/\\i+1^]_C. We also demonstrate that ROBDD[/\\i^]_C (i > 1) and ROBDD[/\\T^,i]_T are not less tractable than ROBDD-L_&infin and ROBDD, respectively. Finally, we develop a compiler for ROBDD[/\\&infin^]_C which significantly advances the compiling efficiency of canonical representations.","doi":"10.24963/ijcai.2017/712","url":"https://ijcai.org/proceedings/2017/712","pdf":"https://ijcai.org/proceedings/2017/0712.pdf","markdown":"https://ijcai.org/proceedings/2017/712.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/712","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Journal track","track":"Journal track","number":712,"pages":{"first":5010,"last":5014},"keywords":["Knowledge Representation, Reasoning, and Logic: Computational Complexity of Reasoning","Knowledge Representation, Reasoning, and Logic: Tractable languages and knowledge compilation","Knowledge Representation, Reasoning, and Logic: Knowledge Representation Languages"],"videos":[],"references":[{"position":1,"raw":"[Bryant, 1986] Randal E. 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