TY - GEN

T1 - On the hardness of approximating the minimum consistent OBDD problem

AU - Hirata, Kouichi

AU - Shimozono, Shinichi

AU - Shinohara, Ayumi

PY - 1996

Y1 - 1996

N2 - 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.

AB - 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.

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U2 - 10.1007/3-540-61422-2_125

DO - 10.1007/3-540-61422-2_125

M3 - Conference contribution

AN - SCOPUS:84947938831

SN - 3540614222

SN - 9783540614227

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 112

EP - 123

BT - Algorithm Theory - SWAT 1996 - 5th Scandinavian Workshop on Algorithm Theory, Proceedings

A2 - Karlsson, Rolf

A2 - Lingas, Andrzej

PB - Springer Verlag

T2 - 5th Scandinavian Workshop on Algorithm Theory, SWAT 1996

Y2 - 3 July 1996 through 5 July 1996

ER -