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Finding Orthogonal Arrays Using Satisfiability Checkers and Symmetry Breaking Constraints

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PRICAI 2008: Trends in Artificial Intelligence (PRICAI 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5351))

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Abstract

Orthogonal arrays are very important combinatorial objects which can be used in software testing and other areas. Mathematical methods for constructing such arrays have been studied extensively in the past decades. In contrast, computer search techniques, in particular exhaustive search methods, are rarely used to solve the problem. In this paper, we present an algorithm which finds orthogonal arrays of given sizes or shows their non-existence. The algorithm is essentially a backtrack search procedure, but enhanced with some novel symmetry breaking (isomorphism elimination) techniques. The orthogonal array is generated column by column, and the constraints are checked by an efficient SAT solver or pseudo-Boolean constraint solver. We have implemented a tool called BOAS (Backtrack-style OA Searcher) using MiniSat and PBS. Experimental results show that our tool can find many orthogonal arrays quickly, especially those with strength higher than 2.

This work is partially supported by the National Natural Science Foundation of China (NSFC) under Grant No. 60673044 and 60633010.

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Author information

Authors and Affiliations

  1. State Key Laboratory of Computer Science Institute of Software, Chinese Academy of Sciences, China

    Feifei Ma & Jian Zhang

  2. Graduate University, Chinese Academy of Sciences, China

    Feifei Ma

Authors
  1. Feifei Ma
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  2. Jian Zhang
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Editors and Affiliations

  1. Japan Advanced Institute of Science and Technology, Asahidai 1-1, 923-12292, Nomi, Japan

    Tu-Bao Ho

  2. Department of Computer Science & Technology, Nanjing University, 22 Hankou Road, 210093, China

    Zhi-Hua Zhou

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© 2008 Springer-Verlag Berlin Heidelberg

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Ma, F., Zhang, J. (2008). Finding Orthogonal Arrays Using Satisfiability Checkers and Symmetry Breaking Constraints. In: Ho, TB., Zhou, ZH. (eds) PRICAI 2008: Trends in Artificial Intelligence. PRICAI 2008. Lecture Notes in Computer Science(), vol 5351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89197-0_25

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  • DOI: https://doi.org/10.1007/978-3-540-89197-0_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89196-3

  • Online ISBN: 978-3-540-89197-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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