On the hardness of approximating the minimum consistent OBDD problem

Kouichi Hirata, Shinichi Shimozono, Ayumi Shinohara

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Citations (Scopus)

Abstract

Ordered binary decision diagrams (OBDDs, for short) represent Boolean functions as directed acyclic graphs. The minimum consistent OBDD problem is, given an incomplete truth table of a function, to find the smallest OBDD that is consistent with the truth table with respect to a fixed order of variables. We show that this problem is NP-hard, and prove that there is a constant ∊ > 0 such that no polynomial time algorithm can approximate the minimum consistent OBDD within the ratio n unless P=NP, where n is the number of variables. This result suggests that OBDDs are unlikely to be polynomial time learnable in PAC-learning model.

Original languageEnglish
Title of host publicationAlgorithm Theory - SWAT 1996 - 5th Scandinavian Workshop on Algorithm Theory, Proceedings
EditorsRolf Karlsson, Andrzej Lingas
PublisherSpringer Verlag
Pages112-123
Number of pages12
ISBN (Print)3540614222, 9783540614227
DOIs
Publication statusPublished - 1996
Event5th Scandinavian Workshop on Algorithm Theory, SWAT 1996 - Reykjavik, Iceland
Duration: 1996 Jul 31996 Jul 5

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1097
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other5th Scandinavian Workshop on Algorithm Theory, SWAT 1996
CountryIceland
CityReykjavik
Period96/7/396/7/5

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Hirata, K., Shimozono, S., & Shinohara, A. (1996). On the hardness of approximating the minimum consistent OBDD problem. In R. Karlsson, & A. Lingas (Eds.), Algorithm Theory - SWAT 1996 - 5th Scandinavian Workshop on Algorithm Theory, Proceedings (pp. 112-123). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1097). Springer Verlag. https://doi.org/10.1007/3-540-61422-2_125