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On the Hardness of Learning Acyclic Conjunctive Queries

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Algorithmic Learning Theory (ALT 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1968))

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Abstract

A conjunctive query problem in relational database theory is a problem to determine whether or not a tuple belongs to the answer of a conjunctive query over a database. Here, a tuple and a conjunctive query are regarded as a ground atom and a nonrecursive function-free definite clause, respectively. While the conjunctive query problem is NP-complete in general, it becomes efficiently solvable if a conjunctive query is acyclic. Concerned with this problem, we investigate the learnability of acyclic conjunctive queries from an instance with a j-database which is a finite set of ground unit clauses containing at most j-ary predicate symbols. We deal with two kinds of instances, a simple instance as a set of ground atoms and an extended instance as a set of pairs of a ground atom and a description. Then, we show that, for each j ≥ 3, there exist a j-database such that acyclic conjunctive queries are not polynomially predictable from an extended instance under the cryptographic assumptions. Also we show that, for each n > 0 and a polynomial p, there exists a p(n)- database of size O(2p(n)) such that predicting Boolean formulae of size p(n) over n variables reduces to predicting acyclic conjunctive queries from a simple instance. This result implies that, if we can ignore the size of a database, then acyclic conjunctive queries are not polynomially predictable from a simple instance under the cryptographic assumptions. Finally, we show that, if either j = 1, or j = 2 and the number of element of a database is at most l (≥ 0), then acyclic conjunctive queries are paclearnable from a simple instance with j-databases.

This workis partially supported by Japan Society for the Promotion of Science, Grants-in-Aid for Encouragement of Young Scientists (A) 11780284.

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Author information

Authors and Affiliations

  1. Department of Artificial Intelligence, Kyushu Institute of Technology, Kawazu 680-4, 820-8502, Iizuka, Japan

    Kouichi Hirata

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  1. Kouichi Hirata
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Editors and Affiliations

  1. Department of Informatics, Kyushu University, Hakozaki 6-10-1, 812-8581, Fukuoka, Japan

    Hiroki Arimura

  2. School of Computing, National University of Singapore, 3 Science Drive 2, 117543, Singapore, Singapore

    Sanjay Jain

  3. School of Computer Science and Engineering, The University of New South Wales, 2052, Sydney, Australia

    Arun Sharma

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Hirata, K. (2000). On the Hardness of Learning Acyclic Conjunctive Queries. In: Arimura, H., Jain, S., Sharma, A. (eds) Algorithmic Learning Theory. ALT 2000. Lecture Notes in Computer Science(), vol 1968. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-40992-0_18

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  • DOI: https://doi.org/10.1007/3-540-40992-0_18

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41237-3

  • Online ISBN: 978-3-540-40992-2

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