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.
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Jia, X., Zhang, J. (2006). A Powerful Technique to Eliminate Isomorphism in Finite Model Search. In: Furbach, U., Shankar, N. (eds) Automated Reasoning. IJCAR 2006. Lecture Notes in Computer Science(), vol 4130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11814771_29
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DOI: https://doi.org/10.1007/11814771_29
Publisher Name: Springer, Berlin, Heidelberg
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