Algorithms and Computation

Volume 1969 of the series Lecture Notes in Computer Science pp 120-131


Reasoning with Ordered Binary Decision Diagrams

  • Takashi HoriyamaAffiliated withGraduate School of Information Science, Nara Institute of Science and Technology
  • , Toshihide IbarakiAffiliated withGraduate School of Informatics, Kyoto University

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We consider problems of reasoning with a knowledge-base, which is represented by an ordered binary decision diagram (OBDD), for two special cases of general and Horn knowledge-bases. Our main results say that both finding a model of a knowledge-base and deducing from a knowledge-base can be done in linear time for general case, but that abduction is NP-complete even if the knowledge-base is restricted to be Horn. Then, we consider the abduction when its assumption set consists of all propositional literals (i.e., an answer for a given query is allowed to include any positive literals), and show that it can be done in polynomial time if the knowledge-base is Horn, while it remains NP-complete for the general case. Some other solvable cases are also discussed.