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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References
Jackson, D., Jha, S., Damon, C.A.: Isomorph-free model enumeration: A new method for checking relational specifications. ACM Transactions on Programming Languages and Systems 20(2), 302–343 (1998)
Boy de la Tour, T., Countcham, P.: An isomorph-free SEM-like enumeration of models. Electr. Notes Theor. Comput. Sci. 125(2), 91–113 (2005)
Moskewicz, M., et al.: Chaff: Engineering an efficient SAT solver. In: Proc. 39th Design Automation Conference, pp. 530–535 (2001)
Audemard, G., Henocque, L.: The extended least number heuristic. In: Proc. of the 1st Int’l Joint Conference on Automated Reasoning, pp. 427–442 (2001)
Sutcliffe, G., Suttner, C.B.: The TPTP problem library – CNF release v1. 2.1. Journal of Automated Reasoning 21(2), 177–203 (1998)
Zhang, H.: An efficient propositional prover. In: McCune, W. (ed.) CADE 1997. LNCS, vol. 1249, pp. 272–275. Springer, Heidelberg (1997)
Gent, I., Smith, B.: Symmetry breaking in constraint programming. In: Proc. ECAI 2000, pp. 599–603 (2000)
Gent, I., Harvey, W., Kelsey, T., Linton, S.: Generic SBDD using computational group theory. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 333–347. Springer, Heidelberg (2003)
Crawford, J.: A theoretical analysis of reasoning by symmetry in first order logic. Technical report, AT&T Bell Laboratories (1996)
Crawford, J., Ginsberg, M., Luks, E., Roy, A.: Symmetry-breaking predicates for search problems. In: Proc. KR 1996, pp. 149–159 (1996)
Slaney, J.: Finite domain enumerator. system description. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814, Springer, Heidelberg (1994)
Zhang, J.: Constructing finite algebras with FALCON. Journal of Automated Reasoning 17(1), 1–22 (1996)
Zhang, J.: Computer search for counterexamples to Wilkie’s identity. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS (LNAI), vol. 3632, pp. 441–451. Springer, Heidelberg (2005)
Zhang, J., Zhang, H.S.: a system for enumerating models. In: Proc. 14th Int’l Joint Conf. on Artificial Intelligence (IJCAI), pp. 298–303 (1995)
Claessen, K., Sörensson, N.: New techniques that improve mace-style finite model finding. In: Proceedings of the CADE-19 Workshop: Model Computation - Principles, Algorithms, Applications (Miami, USA) (2003)
Fujita, M., Slaney, J., Bennett, F.: Automatic generation of some results in finite algebra. In: Proc. 13th Int’l Joint Conf. on Artificial Intelligence (IJCAI), pp. 52–57 (1993)
Eén, N., Sörensson, N.: The MiniSat page. Webpage, Chalmers University (2005), http://www.cs.chalmers.se/Cs/Research/FormalMethods/MiniSat/
Peltier, N.: A new method for automated finite model building exploiting failures and symmetries. J. of Logic and Computation 8(4), 511–543 (1998)
Burris, S., Lee, S.: Small models of the high school identities. Intl. J. of Algebra and Computatio 2, 139–178 (1992)
Fahle, T., Schamberger, S., Sellmann, M.: Symmetry breaking. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 93–107. Springer, Heidelberg (2001)
McCune, W.: MACE 2.0 reference manual and guide. Technical Report No. 249, Argonne National Laboratory, Argonne, IL, USA (2001)
McCune, W.: Mace4 reference manual and guide. Technical Report No. 264, Argonne National Laboratory, Argonne, IL, USA (2003)
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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
Print ISBN: 978-3-540-37187-8
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