Abstract
In the context of equational reasoning, J. Avenhaus and D. Plaisted proposed to deal with leaf permutative equations in a uniform, specialized way. The simplicity of these equations and the useless variations that they produce are good incentives to lift theorem proving to so-called stratified terms, in order to perform deduction modulo such equations. This requires specialized algorithms for standard problems involved in automated deduction. To analyze the computational complexity of these problems, we focus on the group theoretic properties of stratified terms. NP-completeness results are given and (slightly) relieved by restrictions on leaf permutative theories, which allow the use of techniques from computational group theory.
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References
Avenhaus, J. and Plaisted, D.: General algorithms for permutations in equational inference, J. Automated Reasoning 26 (April 2001), 223–268.
Baader, F. and Nipkow, T.: Term Rewriting and All That, Cambridge University Press, 1998.
Babai, L.: Automorphism groups, isomorphism, reconstruction, in R. L. Graham, M. Grotschel and L. Lovasz (eds.), Handbook of Combinatorics, Vol. 2, Elsevier and MIT Press, 1995.
Babai, L., Erdõs, P. and Selkow, S. M.: Random graph isomorphism, SIAM J. Computing 9(3) (August 1980), 628–635.
Barendregt, H. P., van Eekelen, M. C. J. D., Glauert, J. R. W., Kennaway, J. R., Plasmeijer, M. J. and Sleep M. R.: Term graph rewriting, in J. W. de Bakker, A. J. Nijman and P. C. Treleaven (eds.), PARLE’87, LNCS 259, Vol. 2, Springer-Verlag, June 1987, pp. 141–158.
Boy de la Tour, T. and Echenim, M.: On leaf permutative theories and occurrence permutation groups, in I. Dahn and L. Vigneron (eds.), FTP’2003, Electronic Notes in TCS 86, 2003.
Boy de la Tour, T. and Echenim, M.: NP-completeness results for deductive problems on stratified terms, in M. Vardi and A. Voronkov (eds.), LPAR, LNAI 2850, 2003, pp. 315–329.
Boy de la Tour, T. and Echenim, M.: Overlapping leaf permutative equations, in D. Basin and M. Rusinowitch (eds.), IJCAR’04, LNAI, 2004.
Butler, G.: Fundamental Algorithms for Permutation Groups, Lecture Notes in Comput. Sci. 559, Springer-Verlag, 1991.
Furst, M., Hopcroft, J. and Luks, E.: Polynomial time algorithms for permutation groups, in Proceedings 21st Annual Symposium on the Foundations of Computer Science, October 1980, pp. 36–41.
Garey, M. and Johnson, D. S.: Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, CA, 1979.
Hoffmann, C.: Group-Theoretic Algorithms and Graph Isomorphism, Lecture Notes in Comput. Sci. 136, Springer-Verlag, 1981.
Leon, J. S.: Permutation group algorithms based on partitions, I: Theory and algorithms, J. Symbolic Comput. 12(4–5) (1991), 533–583.
Schöning, U. and Pruim, R.: Gems of Theoretical Computer Science, Springer-Verlag, 1998.
Stickel, M. E.: A unification algorithm for associative-commutative functions, J. ACM 28(2) (April 1981), 423–434.
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Boy de la Tour, T., Echenim, M. On the Complexity of Deduction Modulo Leaf Permutative Equations. J Autom Reasoning 33, 271–317 (2004). https://doi.org/10.1007/s10817-004-6244-2
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DOI: https://doi.org/10.1007/s10817-004-6244-2