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 ε > 0 such that no polynomial time algorithm can approximate the minimum consistent OBDD within the ratio n ε 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.
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© 1996 Springer-Verlag Berlin Heidelberg
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Hirata, K., Shimozono, S., Shinohara, A. (1996). On the hardness of approximating the minimum consistent OBDD problem. In: Karlsson, R., Lingas, A. (eds) Algorithm Theory — SWAT'96. SWAT 1996. Lecture Notes in Computer Science, vol 1097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61422-2_125
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DOI: https://doi.org/10.1007/3-540-61422-2_125
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