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A Powerful Technique to Eliminate Isomorphism in Finite Model Search

  • Xiangxue Jia
  • Jian Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4130)

Abstract

We propose a general-purpose technique, called DASH (Decision Assignment Scheme Heuristic), to eliminate isomorphic subspaces when generating finite models. Like LNH, DASH is based on inherent isomorphism in first order clauses on finite domains. Unlike other methods, DASH can completely eliminate isomorphism during the search. Therefore, DASH can generate all the models none of which are isomorphic. And DASH is an efficient technique for finite model enumeration. The main idea is to cut the branch of the search tree which is isomorphic to a branch that has been searched. We present a new method to describe the class of isomorphic branches. We implemented this technique by modifying SEM1.7B, and the new tool is called SEMD. This technique proves to be very efficient on typical problems like the generation of finite groups, rings and quasigroups. The experiments show that SEMD is much faster than SEM on many problems, especially when generating all the models and when there is no model. SEMD can generate all the non-isomorphic models with little extra cost, while other tools like MACE4 will spend more time.

Keywords

Isomorphism scheme symmetry breaking LNH DASH 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Xiangxue Jia
    • 1
    • 2
  • Jian Zhang
    • 1
  1. 1.Laboratory of Computer Science, Institute of SoftwareChinese Academy of Sciences 
  2. 2.Chinese Academy of SciencesGraduate University 

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