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Polynomial-time learning of elementary formal systems

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Abstract

An elementary formal system (EFS) is a logic program consisting of definite clauses whose arguments have patterns instead of first-order terms. We investigate EFSs for polynomial-time PAC-learnability. A definite clause of an EFS is hereditary if every pattern in the body is a subword of a pattern in the head. With this new notion, we show that H-EFS(m, k, t, r) is polynomial-time learnable, which is the class of languages definable by EFSs consisting of at mostm hereditary definite clauses with predicate symbols of arity at mostr, wherek andt bound the number of variable occurrences in the head and the number of atoms in the body, respectively. The class defined by all finite unions of EFSs in H-EFS(m, k, t, r) is also polynomial-time learnable. We also show an interesting series ofNC-learnable classes of EFSs. As hardness results, the class of regular pattern languages is shown not polynomial-time learnable unlessRP=NP. Furthermore, the related problem of deciding whether there is a common subsequence which is consistent with given positive and negative examples is shownNP-complete.

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Author information

Authors and Affiliations

  1. Human Genome Center, Institute of Medical Science, University of Tokyo, 4-6-1 Shirokanedai, Minato-ku, 108-8639, Tokyo, Japan

    Satoru Miyano

  2. Department of Informatics, Kyushu University 33, 812-8581, Fukuoka, Japan

    Ayumi Shinohara

  3. Department of Artificial Intelligence, Kyushu Institute of Technology, 820-8502, Iizuka, Japan

    Takeshi Shinohara

Authors
  1. Satoru Miyano
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  2. Ayumi Shinohara
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  3. Takeshi Shinohara
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Corresponding author

Correspondence to Satoru Miyano.

Additional information

Satoru Miyano, Dr. Sci.: He is a Professor in Human Genome Center at the University of Tokyo. He obtained B.S. in 1977, M.S. in 1979, and Dr. Sci. degree all in Mathematics from Kyushu University. His current interests include bioinformatics, discovery science, computational complexity, computational learning. He has been organizing Genome Informatics Workshop Series since 1996 and has served for the chair/member of the program committee of many conferences in the area of Computer Science and Bioinformatics. He is on the Editorial Board of Theoretical Computer Science and the Chief Editor of Genome Informatics Series.

Ayumi Shinohara, Dr. Sci.: He is an Associate Professor in the Department of Informatics at Kyushu University. He obtained B.S. in 1988 in Mathematics, M.S. in 1990 in Information Systems, and Dr. Sci. degree in 1994 all from Kyushu University. His current interests include discovery science, bioinformatics, and pattern matching algorithms.

Takeshi Shinohara, Dr. Sci.: He is a Professor in the Department of Artificial Intelligence at Kyushu Institute of Technology. He obtained his B.S. in Mathematics from Kyoto University in 1980, and his Dr. Sci. degree from Kyushu University in 1986. His research interests are in Computational/Algorithmic Learning Theory, Information Retrieval, and Approximate Retrieval of Multimedia Data.

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Miyano, S., Shinohara, A. & Shinohara, T. Polynomial-time learning of elementary formal systems. New Gener Comput 18, 217–242 (2000). https://doi.org/10.1007/BF03037530

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  • DOI: https://doi.org/10.1007/BF03037530

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