TY - GEN

T1 - Learnability of exclusive-or expansion based on monotone DNF formulas

AU - Takimoto, Eiji

AU - Sakai, Yoshifumi

AU - Maraoka, Akira

N1 - Publisher Copyright:
© 1996, Springer Verlag, All Rights Reserved.

PY - 1996

Y1 - 1996

N2 - The learnability of the class of exclusive-or expansion based on monotone DNF formulas is investigated. The class consists of the formulas of the form (Formula presented), where (Formula presented) are monotone DNF formulas. It is shown that any Boolean function can be represented as an formula in this class, and that the representation in the simplest form is unique. Learning algorithms that learn such formulas using various queries are presented: An algorithm with subset and superset queries and one with membership and equivalence queries are given. The former can learn any formula in the class, while the latter is proved to learn formulas of bounded depth, i.e., formulas represented as exclusive-or of a constant number of monotone DNF formulas. In spite of seemingly strong restriction of the depth being constant, the class of formulas of bounded depth includes functions with very high complexity in terms of DNF and CNF representations, so the latter algorithm could learn Boolean functions significantly complex otherwise represented.

AB - The learnability of the class of exclusive-or expansion based on monotone DNF formulas is investigated. The class consists of the formulas of the form (Formula presented), where (Formula presented) are monotone DNF formulas. It is shown that any Boolean function can be represented as an formula in this class, and that the representation in the simplest form is unique. Learning algorithms that learn such formulas using various queries are presented: An algorithm with subset and superset queries and one with membership and equivalence queries are given. The former can learn any formula in the class, while the latter is proved to learn formulas of bounded depth, i.e., formulas represented as exclusive-or of a constant number of monotone DNF formulas. In spite of seemingly strong restriction of the depth being constant, the class of formulas of bounded depth includes functions with very high complexity in terms of DNF and CNF representations, so the latter algorithm could learn Boolean functions significantly complex otherwise represented.

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U2 - 10.1007/3-540-61863-5_30

DO - 10.1007/3-540-61863-5_30

M3 - Conference contribution

AN - SCOPUS:84949220231

SN - 3540618635

SN - 9783540618638

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

SP - 12

EP - 25

BT - Algorithmic Learning Theory - 7th International Workshop, ALT 1996, Proceedings

A2 - Arikawa, Setsuo

A2 - Sharma, Arun K.

PB - Springer Verlag

T2 - 7th International Workshop on Algorithmic Learning Theory, ALT 1996

Y2 - 23 October 1996 through 25 October 1996

ER -